The Met Office has issued an amber warning for Sunday (July 17) and red warnings for Monday and Tuesday (July 18 and 19) saying that there is a danger to life.
With the hot weather likely to cause delays, National Rail advises passengers to regularly check National Rail Enquiries before they set off.
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James Dean, Network Rail's West Coast South route director, said: “Keeping passengers moving is always our top priority. But we want people to be prepared.”
Mr Dean added: “If the soaring temperatures do lead to us having to put in place slower speeds for safety reasons, please bear with us while our engineers work to fix the problem. It may mean some journeys take longer.”
Direct sunlight can cause track temperatures to reach more than 50°C as steel rails absorb heat easily.
Trains will run at slower speeds to put less strain on the rails which can bend and, in serious cases, buckle.
The network of 25,000 volt electric cables which power trains on the West Coast main line is also susceptible to high temperatures.
The cables can cause the steel wires to overheat and then hang too low - getting caught on passing trains and knocking out their electricity supply.
National Rail also advises to carry water while travelling over the next week.