It's largely down to heat capacity, mostly that of water. Water requires a good bit of energy to heat up by a given amount, and it has to lose that same energy to cool down; so even though the amount of solar heating is lowest in December, the oceans and other bodies of water are still holding onto heat from summer, and will continue to cool until the rate of solar heating surpasses the rate of cooling at some point in spring.

Heat is distributed pretty widely in the atmosphere, the poles are a fair bit warmer than they would be without an atmosphere and oceans, but the transport still isn't perfect so there is a gradient (compare to somewhere like Venus, which has a thicker atmosphere of mostly greenhouse gasses and so very little temperature variation on the surface, other than that caused by altitude).