Will a Galileo's Thermometer containing liquid paraffin explode in my car if the temperature is above 35 degrees Celsius?
Do not confuse the flash point with the autoignition temperature.

I don't know what atmosphere you have inside the thermometer, but either way I think it's hardly the case that you reach the autoignition temperature of paraffin (gasoline undergoes autoignition at 246-280 °C).