With temperatures expected to exceed 40C across parts of the UK, Professor Penny Endersby said it was crucial that people took action to protect themselves as they would during severe storms or gales.
The Met Office has issued its first ever red warning for extreme heat, covering swaths of England. An amber warning is also in place today and tomorrow across much of southern and eastern Scotland and the central belt.
The rise in temperatures has forced the UK Health Security Agency to issue a level 4 heat-health alert - described as an "emergency.”
But Prof Endersby, chief executive of the Met Office, said she feared some people were taking the warnings seriously.
"They think we shouldn’t be telling them to worry about heat the way they should when we tell them to worry about storms or wind,” she told the BBC.
"These temperatures are unprecedented and we’re not used to dealing with them - heat causes many hundreds or thousands excess deaths, so people need to follow the advice of keeping the shade, keeping cool and hydrated."
Temperatures are set to spike even higher on Tuesday, with some forecasts of 43C in south-east England. The forecast for Hawick in the Scottish Borders also suggests that the mercury could hit 34C tomorrow afternoon.
If realised, that would easily overtake Scotland’s all-time record temperature of 32.9C, which was recorded in Greycrook in the Borders in August 2003.