Gas heating is to be eliminated from all Historic Environment Scotland (HES) buildings, including Edinburgh Castle, by 2032.
HES said it aimed to be "net-zero" by 2045 in line with the Scottish government's target.
The organisation plans to reduce the amount of visitor vehicles by 2028 by creating parking hubs where it has clusters of properties.
Low carbon "district heating" systems could also be used on some sites.
District heating takes energy released as heat and transfers it elsewhere using highly insulated pipes. HES said it could be installed on properties in highly populated areas.
The public body is one of Scotland's biggest operators of tourists sites that attract millions of visitors each year.
It manages more than 300 properties, including Stirling Castle and Linlithgow Palace.
Jane Ryder, chair of HES, said: "In the past year, international heritage experts have come to Scotland to work with us to develop pioneering methods to better understand the climate change threat to World Heritage sites.
"In addition to piloting some ground-breaking approaches, we've hosted the launch of a new international network which has united cultural heritage organisations from across the globe to take action against climate change.
"And now we're setting out our most ambitious climate change plans to date. The Climate Action Plan will transform how we operate as an organisation, increasing resilience and making our business more effective and efficient while placing environmental responsibility at the heart of everything we do."
The plan sets out how HES aims to reduce its carbon footprint over the coming years.
It intends to reduce its vehicle fleet by 30% by 2025 and, where practicable, have fully electric cars.
Investment will also be made in cycling infrastructure for staff and visitors.
The use of taxis will be heavily curtailed with an aim to reduce use by 80% by 2022.
Culture Secretary Fiona Hyslop said: "The historic environment has a critical role to play in our response to the global climate emergency.
"This Climate Action Plan recognises the scale of the challenge we face and the need for immediate and widespread action.
"I welcome the commitment Historic Environment Scotland is making to meeting our ambitious emissions targets and look forward to seeing the results of its work in the coming years."