No. Do not use hot water.
The Brita standard filter is rated for cold tap water only. The acceptable water temperature range is 32°F to 85°F (0°C to 29°C). Using water outside this range, especially hot water, can damage the filter media and is not recommended.
If you have used hot water, replace the filter. The filter's performance is not certified for water outside the specified temperature range.
Safety note: The Brita standard filter is not a purifier. Do not use it with water that is not microbiologically safe without proper disinfection before or after filtration.