Between 11am and 3pm, people are being advised to stay indoors due to safety concerns as extreme temperatures are likely to sweep across the country on Tuesday.
Today is set to be the hottest day of the year and, potentially, ever, as there is an amber weather warning in place for much of the country. In Scotland, this is mainly in the south and east.
"This is unprecedented so it brings with it a number of potential dangers which is why we are saying to people to think very carefully about travelling and if they can avoid travelling, to do so and if they can think very carefully about not being in direct sunlight between 11am and 3pm as we know the effect this can have.”
It is possible trains may have to operate more slowly as a result of the extreme weather, according to the justice secretary.
He said: "Train operators are taking precautions to make sure that can’t have as much an impact as it otherwise would.”
If people do travel, Mr Brown said they should take fluids and sun cream with them and make sure they are able to find shade safely and look after vulnerable people who are potentially travelling.
The areas where the amber warning applies the Scottish Government are concerned about are Dundee, Edinburgh, the Lothians, Fife, Perth, Clackmannanshire, Falkirk, eastern parts of Lanarkshire, the Borders and Dumfries and Galloway.
“Generally, the further south and east you go are the areas we are likely to see the highest temperatures,” said Mr Brown.
Mr Brown said this warm weather acts as a “learning experience” for the Scottish Government to make sure they can mitigate future heat impacts.
Friends of the Earth warned a third runway installed at Heathrow airport would “wipe out” targets on tackling emissions.
The justice secretary said it is “a decision for the UK Government to take” despite the Scottish Government previously backing the runway due to better connectivity to Scotland.