The Met Office has forecast temperatures will reach as high as 33C.
That peak would make it the hottest Scottish summer in 12 years.
Hotter temperatures are eight times as likely as cooler temperatures, the Met Office has claimed.
The best of the weather is tipped for late June to August.
The Met Office June-August forecast said: “For June-August, above-average temperatures are more likely than below-average temperatures.
“The probability the UK average temperature for June-August will fall into the warmest of our five categories is 40 per cent.
“The coldest of our five categories is around 5 per cent.
“The likelihood of above-average temperatures is greater than usual. The Met Office long-range prediction system shows a slightly increased chance of high-pressure patterns across the UK.”
Weather Outlook forecaster Brian Gaze said: “The warmest summer since 2006 is a possibility after recent years saw a series of disappointing summers.
Met Office records show Britain’s average summer temperature is 14.3C.
The hot weather is set to arrive as the UK gears up for the World Cup and Wimbledon.
Temperatures in Edinburgh and Glasgow are set to push towards 20C over the coming week.
A spokesperson from the Met Office said: “Many places will see warm spells of sunshine after any early mist has cleared this week.
“Some heavy showers will develop across Scotland and northern England later where it will be fairly cloudy.”