Caledonian Sleeper said it planned to operate its normal cross-Border services on Wednesday night after being forced to cancel all its trains at around midnight on Tuesday because of fires and damage to the west coast main line, which they use.
Passengers on several services were able to spend the night aboard the trains, some in stations.
Those trying to travel by rail faced chaos at stations on Wednesday morning after temperatures hit 40C on Tuesday, a new UK record, causing damage to overhead wires, tracks and signalling systems.
Many trains between London Euston and Scotland were cancelled, while no trains were running north of Birmingham to Wolverhampton.
Avanti West Coast said services from London Euston were cancelled due to ongoing repair work following damage caused by fires in the Hatch End area of north-west London on Tuesday.
A spokesman said: “Train services are severely disrupted across our network as a result of damage to the overhead wires at multiple locations due to yesterday’s extreme heat.”
The spokesman added: "Whilst the lines have reopened, our services are still subject to delay and cancellation.
"The big issue we have is with displaced rolling stock and train crew as a result of yesterday’s heat and the disruption this morning.
"We have extended the ticket window until Friday, so customers with tickets for Monday, Tuesday and today can use their ticket to travel at anytime tomorrow until midday on Friday."
Network Rail said passenger numbers on Tuesday were around 40 per cent lower than the same day last week.
The East Coast Main Line, the main rail artery connecting London and Edinburgh via Peterborough, Doncaster, York, Darlington, Durham and Newcastle, was damaged on Tuesday after a fire spread on to the track near Sandy.
The Caledonian Sleeper also cancelled services amid reports that guests were kept on an Inverness train overnight without departing due to the extreme conditions. They tweeted: “As a result of network related issues on both the West and East Coast Mainlines, early morning services to and from London and central Scotland are being cancelled by operators.
“For guests who travelled south from Inverness, Aberdeen and Fort William we advise that where possible you should return on our services and for guests on our services starting from Glasgow, Edinburgh and Euston, we advise you to return home
“Where this is not possible and for those currently in a location away from home, please continue to review our service alterations website page for further updates. Once confirmation is received of services operating on each Mainline we will post updates.
“Please once again accept our sincerest apologies for the inconvenience caused by the incidents related to the extreme temperatures. “
ScotRail trains have returned to normal this week with almost 700 more services running each day.
The train operator has advised passengers to check times before travel as trains will revert back to this year’s May timetable from today.