Conditions on other routes will be closely monitored with further changes to service possible.
Additional response staff will be out on the network to respond to incidents, but the heat makes working conditions challenging for them too.
Sam MacDougall, operations director for Network Rail, said: “Closing the line to traffic is always a last resort but it is the right thing to do to keep people safe on Tuesday given the unprecedented heatwave forecast. The forecast temperatures are well above those which our infrastructure is designed, and safety must come first.
“On Monday we are reducing the speed at which trains can run which will limit the number of trains running and extend journey times significantly so we’re asking passengers to only travel if absolutely necessary.
“The best way to keep everyone safe and prevent passengers from becoming stranded on trains in the extraordinary heat is to proactively close the East Coast Main Line routes south of York and Leeds during the very hottest temperatures. I am sorry for the disruption this will cause.”
Jason Webb, director of customer information at trade body Rail Delivery Group, said: “These are extreme temperatures and while the whole industry is pulling together to deliver the best possible service under the circumstances, we must ask people to only travel if absolutely necessary.
“If you have no choice but to travel on lines that are open, please take all sensible precautions to keep yourself safe and well, like bringing water for your journey.
“If your train is disrupted and you choose not to travel then you are eligible for a fee free refund. Some operators will also offer customers the ability to travel either Wednesday or Thursday if they prefer to delay their travel – please check with your operator. We are sorry for the disruption caused.”
Remember to drink plenty of water during this hot weather if you absolutely have to travel on other lines.
You can fill up your reusable water bottle at one of the free cold-water fountains at Britain’s biggest railway stations.