Only a tiny amount of atmospheric heat comes from inside the earth. The overwhelming majority comes from radiation from the sun.
In general terms there is a lag in surface temperatures behind the sun's movement, so min and max temps are usually after the times for min and max incoming solar radiation.
Coldest days are after the winter solistice, and hottest after midsummer. Hurricanes, for example, are heat driven, and the hurricane season is about July through October. not May through August.
Bristol hands refer to your Met notes.
Dick W