Edinburgh is forecast to be hotter than Rio de Janeiro on Tuesday, with the mercury potentially reaching 28c.
Met Office meteorologist Luke Miall said the Capital will be very close to experiencing a heatwave between Monday and Thursday, but will likely fall just short.
He said that, for a heatwave to occur in Scotland, there needs to be three days in a row of recorded maximum daily temperatures at 25c or above.
The maximum temperature recorded in Edinburgh today was 24.7c - the hottest of the year so far - at the Royal Botanic Garden.
Mr Miall said that on Tuesday, early cloud will quickly melt away for a day of "strong sunshine," adding: "Temperatures will be in the region of 27c, possibly 28c, so it will be turning quite hot.
"We are expecting to get that sort of heat right across eastern Scotland."
Tuesday will be the hottest day in Edinburgh so far this year, while Rio de Janeiro in Brazil is forecast to reach a maximum of 27c according to the Met Office.
Temperatures have already exceeded 28c elsewhere in Scotland this year, with 30c recorded in Achnagart in the west Highlands in June.
Mr Miall says the most likely part of Scotland to get an official heatwave this week will be Aberdeenshire, with Aboyne recording 25.5c on Monday.
But he warned of a risk of thunderstorms from Tuesday night into Wednesday in Edinburgh, given the heat and humidity forecast.
Any bad weather overnight in the Capital should be clear by early Wednesday morning and the rest of the day should be mostly dry, with fresher air and temperatures of about 24c.
Thursday could get warmer again, with the mercury expected to rise back up to about 26c. There will be more risk of thunder on Thursday.
Mr Miall says that, by Friday, the weather will start to cool down, although by the weekend it will likely still be in the high teens.