Why are January and February the coldest months although 21 December is the shortest day? My question deals with the northern hemisphere only, obviously. It seems to me that January and February are the coldest months of the year. Water temperature is even more 'retarded': the seas are coldest in February and March. Since 21 December is the shortest day of the year, why isn't (the end of) December the coldest time of the year, both in air and water temperature?
Short answer: air, land and water take a while to cool down (or rise in temperature; we see the same thing happening with July and August being the warmest months on average – not June, while June 21st is the longest day). In December, the fall just ended, and everything is relatively warm.
Also, depending on how far North you go, the difference between day length in December, January and February isn't that much. See this graph from Wikipedia: