The Met Office said there was “a good chance” that the Scottish record of 32.9C (91.2F) could be broken in the south east of the country.

An amber warning for extreme heat remains in force across parts of Scotland until midnight.

Most of Scotland saw high temperatures on Monday with Edinburgh and Aberdeenshire passing the 30C mark.

The existing Scottish record was set at Greycrook in the Scottish Borders on 9 August 2003.

Met Office forecaster Mark Wilson said: “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.”

On Monday afternoon, the temperature rose to 31.3C (88.3F) in Aboyne in Aberdeenshire, and Leuchars in Fife, the Met Office said.

Elsewhere, the Royal Botanic Garden in Edinburgh recorded 30.8C (87.4F), and the mercury peaked at 29.9C (85.8F) in Aviemore.

A national emergency has been declared in the UK, with an unprecedented red extreme heat warning issued in England.

Justice Secretary and lead minister for resilience Keith Brown said the Scottish government was getting regular updates from transport providers, the NHS and emergency services on the impact of the heatwave.

He said: “I would urge people to think about whether they need to travel and if they do, make sure they’re properly equipped, and plan their journey in advance.

“Rail passengers and drivers should make sure they have water, sunscreen, hats and sunglasses and have a fully charged phone in case of any difficulties.

“When temperatures increase, it’s important to monitor forecasts and follow public health advice, including staying hydrated and drinking plenty of fluids and avoiding excess alcohol.”

Another day of weather-related disruption is expected on the railways with LNER cancelling all trains south of York and Avanti West Coast and Transpennine Express running a much reduced service.

On Monday the heat caused the overhead lines between Glasgow Queen Street low level and Hyndland to “sag” and speed restrictions were put in place that affected all ScotRail services.

Elsewhere, Loch Lomond and The Trossachs National Park has urged care around water, emphasising the risk of cold water shock.

Scottish Water has asked the public to be as efficient as possible with water use, including using watering cans rather than hoses in gardens, not to fill up paddling pools and to take shorter showers.

And the Scottish Environment Protection Agency (Sepa) has advised businesses to reduced their water usage to help current water scarcity issues.

The risk to health of high temperatures has also prompted the release of public health advice including drinking plenty of fluids, keeping out of the sun and avoiding exercise in the hottest part of the day.

Concern is highest for the very young, those with underlying health conditions, and for the elderly.

Climate change, which has pushed up global temperatures by 1.2C on pre-industrial levels, is making heatwaves longer, more intense and more likely.

The weather alert north of the border affects: