The current heatwave could become the new normal for UK summers by 2040 because of climate change, MPs say.
The Environmental Audit Committee warns of 7,000 heat-related deaths every year in the UK by 2050 if the government doesn't act quickly.
Higher temperatures put some people at increased risk of dying from cardiac, kidney and respiratory diseases.
The MPs say ministers must act to protect people - especially with an ageing population in the UK.
Scientists differ on whether the current global rash of heatwaves is definitely caused by climate change.
But they broadly agree that future heatwaves will be hotter and more frequent thanks to carbon emissions.
The MPs highlight a warning from the Met Office that UK summer temperatures could regularly reach 38.5C by the 2040s.
How can people be protected?
The government says it is committed to cutting carbon emissions, although it is not on track to meet its targets.
The MPs say current plans will not stop buildings overheating, and ministers should be smarter about heat-proofing the UK.
Tougher rules are needed to ensure homes and transport networks can deal with extreme heat.
And local councils should plant trees and keep green spaces to provide cool air.
What about the NHS?
During the 2003 heatwave, excess deaths in nursing homes in parts of the UK rose by 42%.
The MPs want hospitals and care homes inspected to check they can cope with scorching heat.
Committee chair Mary Creagh said: "Heatwaves threaten health, wellbeing and productivity.
"The government must stop playing pass-the-parcel with local councils and the NHS, and develop a strategy to protect our ageing population from this increasing risk."
Which homes are at risk?
In a densely populated city, temperatures are higher.
Homes built in the 1960s and 1970s present a particular risk, as can flats with windows that are small, hard to open or face the same way.
The committee complains there is no regulation to prevent overheating in buildings.
It wants the government to stop supporting the building of modular homes, which are factory-made then bolted together. It also calls for shading structures on buildings.
Analysis by BBC Reality Check
Following the heatwave in August 2003, statisticians linked 2,091 deaths to the unusually high temperatures.
Heat isn't a cause that appears on anyone's death certificate. So how do we measure the death-toll of a heatwave?
Excess mortality figures are arrived at by comparing the death rate in a given period to the average for that period in previous years.
We don't know that heat was a factor in all of those deaths - just that there were that many more deaths than the average for the same period over the previous five years.
Death rates in summer tend to be relatively stable so this was an unusual spike.
Researchers used this 2,091 figure as a baseline when calculating how many more people could die in heatwaves by 2050. They estimated there would be an increase of more than 200%, giving the 7,000 figure.
The Office for National Statistics doesn't regularly look at how many deaths are linked to hot weather, but it does regularly publish excess winter mortality data. More people die in winter than in summer because of cold weather and higher rates of infectious illnesses such as flu. In the winter of 2016-17, there were 34,300 excess deaths compared with the death rate in the summer.
Will transport be hit?
The report says only 50% of UK motorways and major roads are surfaced with material that can withstand the kind of summer temperatures the country is beginning to experience regularly.
During June's heatwave, railway tracks buckled causing cancellations and delays.
How should offices and schools adapt?
High heat reduces productivity. Workers arriving sweating to the office take time before they're ready to do the job. People working outside find themselves doing less and needing more breaks.
The committee says Public Health England should tell employers to relax dress codes and allow flexible working in heatwaves.
Maximum workplace temperatures should also be introduced, especially for physical work.
In schools, head teachers should be advised about safe classroom temperatures. And they should relax school uniform policy during hot weather.
A recent study suggested wealthy private schools that could afford air conditioning would increase the relative exam success of their pupils during summer heat.
Should we fear heat island?
Cities can be up to 10C hotter than the surrounding countryside because hard surfaces absorb heat during the day and give out heat at night. This is the heat island effect.
If people get too hot in bed, it prevents them recovering from the previous day's heat.
Yet the government's planning framework makes no mention of the heat island effect.
And ministers withdrew funding for local authority climate change adaptation officers, who were working on the issue.
The report calls for towns and cities to be adapted to more frequent heatwaves.
What about water supplies?
There have been consistent demands for water companies to store more water, especially in dry south-east England, and to plug leaks. New homes should have to use water more efficiently, MPs say.
Kathryn Brown, head of adaptation at the Committee on Climate Change, said: "Water shortages are a concern. We can expect greater water deficits across the country, including in cooler wetter areas like north-west England.
"The area of land well suited to the production of water-intensive crops, such as rain-fed potatoes, could decline by over 80% by the 2050s."
Will we get out-of-season heatwaves?
The committee says the government's heatwave alert system runs only from June to September, so vulnerable people will not be warned about unseasonal heatwaves.
The MPs heard that alerts are put out only if approximately 30°C is reached, even though Public Health England said heat-related deaths began at upwards of 25°C.
What about cold weather?
In the UK, many more preventable deaths happen because of cold weather than hot weather, but the government has failed to deliver its targets for insulating homes.
If the UK's winters get warmer, as generally predicted, winter deaths will be reduced. But in a year like this one, the UK has suffered extremes of cold and heat.
Both heat-related and cold-related health burdens in future will be amplified by population ageing.
How will heatwaves affect poor countries?
Charities point out that the UK's challenges from future heatwaves will be dwarfed by those in poor nations, which haven't caused the climate problem.
A study by Prof Richard Tol, at the University of Sussex, suggests poorer countries are likely to see their economic growth slowed because they depend on agriculture and outdoor work.
His study says nations with hot climates will need economies three times larger than cooler countries if they are to withstand significant temperature rises.
He says policymakers must consider poverty reduction as a crucial element of climate policy.
What does the government say?
An official told BBC News the government would "carefully consider" the report and would keep taking "robust action to ensure our country is resilient and prepared".
The "long-term plan for climate change adaptation" will see work and investment to protect food and water supplies, businesses and communities, the official said.
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Correction 25 September 2018: This article has been amended to clarify that scientists broadly, not universally, agree that future heatwaves will be hotter and more frequent thanks to carbon emissions.