This will see the two towns bask in more sunshine than in southern France and Spain.
The mercury will be at its highest tomorrow when temperatures of 30C degrees are forecast for parts of Tunbridge Wells and Tonbridge.
Elsewhere in the South East, temperatures could reach 34C degrees by Thursday.
The balmy weather is being caused by a plume of warm air coming from the south-west Atlantic, Spain and Portugal.
Met Office forecaster Luke Miall said: “We’ve got high pressure to the South East of the UK over the next few days which is going to be drawing our air up from the continent, and the warmer climates of France and Spain.”
The hottest day of the year so far was 28.9 degrees, which was reached last month, but Mr Miall explained: “Thursday will probably be the hottest day, in the region of 33 or 34 degrees.”
He added that the record for June in the UK came in 1976 when temperatures reached 35.6C degrees.
The heatwave is predicted to last until Friday before temperatures are expected to drop over the weekend.
“By Saturday most places will be seeing the fresher air coming across for the weekend, so although it might still be humid at times, I think generally temperatures will be falling below heatwave,” added Mr Miall.
With the dry and sunny weather expected and the Government’s Covid-19 alert level lowered to three, emergency services across the country are urging people to continue to respect the two-metre social-distancing restriction.