Millions more people are working from home to avoid severe disruption to transport networks caused by soaring temperatures.
Road traffic and public transport usage dropped on Monday after people were urged to avoid unnecessary travel.
Network Rail said the number of passengers using major stations across Britain on Monday was around 20% down on a week ago.
Location technology firm TomTom said road congestion at 9am was lower in most UK cities than at the same time last week.
In Glasgow, congestion levels dropped from 17% to 12%.
The figures reflect the proportion of additional time required for journeys, compared with free-flow conditions.
Temperatures have soared above 30C in Scotland as the country swelters in a heatwave.
The Met Office has issued an amber weather warning of “extreme heat” in eastern, southern and central parts of Scotland which is in force until midnight on Tuesday.
On Monday afternoon, the mercury rose to 31.3C in Aboyne in Aberdeenshire, and Leuchars in Fife, the Met Office said. Meanwhile the Royal Botanic Garden in Edinburgh recorded 30.8C, and the mercury peaked at 29.9C in Aviemore.
Temperatures have not broken Scotland’s 9 August 2003 record of 32.9C at Greyrcrook in the Scottish Borders, but forecasters said that may happen on Tuesday.
Met Office forecaster Mark Wilson said: “The temperature has not broken Scotland’s all time record but there is a chance of reaching that tomorrow.
“Across southern parts of Scotland we could see up to 35C, that’s the top end. If we see that it would be an all time record for Scotland by a couple of degrees so we will be watching closely.”
Train speed restrictions imposed by Network Rail to reduce the chances of tracks buckling in the heatwave caused delays and cancellations.
Many operators are running a heavily reduced timetable on Monday and Tuesday, including Avanti West Coast and CrossCountry. LNER will run no trains from south of York and south of Leeds to London King’s Cross today.
Kevin Groves, chief spokesman for Network Rail, said journeys which typically take two hours could take “more than four hours” as emergency measures have been brought in to prevent trains derailing.”
Network Rail confirmed train speed restrictions will be in place between Glasgow Central and Edinburgh Waverley; Dumfries and Carlisle as well as Glasgow Queen Street and Aberdeen; Inverness; Oban and Fort William and Edinburgh Waverley and North Berwick, with delays of around 10 minutes expected.
In Glasgow, ScotRail warned rail passengers they may face delays as overhead lines were tripping and resetting due to the heat between Glasgow Queen Street Low Level and Hyndland.
Network Rail Scotland tweeted that it was investigating an electrical fault with the overhead lines between Glasgow Queen Street Low Level and Hyndland “caused by the extreme heat” and said the electricity supply will remain switched off until the repairs are carried out.
Meanwhile, Scotland’s First Minister Nicola Sturgeon told people to “follow sensible advice” as temperatures soar.
The First Minister tweeted: “The next couple of days are set to be exceptionally hot. Please take care and follow sensible advice – keep out of direct sun; stay well hydrated; and look out for others who may be suffering from the heat.”
Jake Kelly, also from Network Rail, warned of travel disruption across the country. He told BBC Radio 4’s Today programme the return of normal services on Wednesday “will depend on the damage that the weather does to the infrastructure”.
Council gritters were on stand-by to spread light dustings of sand on melting roads.
The RAC anticipated that the number of vehicle breakdowns on Monday and Tuesday could be up to a fifth higher than normal.
Spokesman Rod Dennis said the increase in callouts will “put pressure on all breakdown services” as he advised drivers to carry an “emergency kit” such as water, non-perishable food, sun protection and any medication required.
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