The yellow ‘be aware’ warning is mainly for the west of the county, with the best of the weather in the east.
Most of the county is seeing plenty of sunshine today with highs of 20degC.
The temperature is set to be in the mid to high teens tomorrow which could trigger off thunderstorms in the afternoon.
The main threat is in the south-west of England but West Sussex could be affected.
The heaviest showers and thunderstorms could produce 20mm of rain within an hour.
The Met Office says that Sunday and Bank Holiday Monday are set to be mainly cloudy with the chance of the sun breaking through on occasion.
There were concerns about a large bank of rain moving across from Europe on Monday but the current forecast is that this is unlikely to move as far west as Sussex.
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