An update meant the Met Office 'shifted north and westward' a yellow warning that was due to cause problems in Edinburgh and Lothians, and now runs from the Borders to the Highlands, taking in Glasgow and much of central Scotland.
Travel disruption is also a possibility as the storms take hold, according to the forecaster.
There is a "small chance that homes and businesses could be flooded quickly" during thundery downpours, with lightning strikes, hail and strong winds all expected.
Power cuts and difficult driving conditions are also possible, and 20mm (0.8in) to 30mm (1.2in) of rain could fall in an hour in some areas.
Met Office severe weather warnings cover large parts of England, Wales and Scotland across Tuesday and Wednesday.
More normal conditions are forecast to return from Thursday, with sunny spells and showers forecast for many.