The official heat warning covering all Sussex now lasts until Friday, with shade temperatures likely to reach at least 30C at Gatwick on Wednesday.
It's a call from the Met Office to public authorities, so they can take action to protect vulnerable people.
The level-three "amber" alert means there's a risk to health from the high temperatures.
The warning, which is going out to health professionals, councils and other public bodies, has extended by a day the chance that temperatures could have "a significant effect on health".
The Met Office said there is a 90% probability, or a 9-in-10 chance, that two consecutive days' daytime temperatures will measure 32C, and the night between won't fall below 16C.
These criteria are expected to be met between midnight on Monday night / Tuesday morning, and 9am on Friday (extended from 9am Thursday).
Forecasters advised members of the public in Sussex to take these actions:
- Close curtains on rooms that face the sun to keep indoor spaces cooler
- Remember it may be cooler outdoors than indoors.
- Look out for others, especially older people, young children and babies and those with underlying health conditions.
- Drink plenty of fluids but avoid excess alcohol
- Dress appropriately for the weather
- Slow down when it is hot.
According to the Met Office, the present settled weather is expected to continue through much of the coming week.
Current indications are then for temperatures falling below trigger criteria into the weekend as cloud and thundery rain spreads north.
They promised that an update will be issued when the alert level changes.
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