The force said “most” parts of the South West of England are now on wildfire alert.
“The peak is predicted to be on Friday, with the Fire Severity Index as shown in the image set at either high or very high for the majority of Devon and Cornwall,” police said.
“The Initial Spread Index is set to reach 'high danger' conditions. Some ignitions are possible, resulting in moderate to high wildfires, particularly in cut grass and crops.
“The daytime winds are variable in both speed and direction rising to around 25kph from the East on Friday.
“These could be troublesome if there is an ignition.”
Tourists were warned to avoid using outdoor barbecues or starting camp fires and to dispose of cigarettes safely.
In London, Royal Parks have also renewed its warnings not to use barbecues in sunny weather because of their potential to spark fires.
The capital saw temperatures of 28C on Thursday, after reaching a record-breaking high of 32.2C at London's Heathrow earlier this week.
The extreme heat has also seen train lines buckle and prompted the Met Office to issue an extreme heat warning.
Warning are in place in southern England, Wales and Northern Ireland until Friday, with temperatures predicted to reach highs of 33C in some areas.
The dry heat is expected to last until the weekend when the Met Office has forecast thunderstorms “moving up from the south” and “heavy and thundery showers on Sunday and Monday”.