The Earth heat storage is mostly in the oceans
When there is too much heat stored in the oceans, the ocean currents carry the warm water into the Polar Regions and that melts Polar Sea Ice and turns on snowfall and cooling. When there is not enough heat in stored in the oceans, the ocean currents carry the not warm enough water into the Polar Regions and that allows the Polar Oceans to freeze over and turn off the snowfall and turn off the cooling.
This process switches on and off to keep the Earth Temperature bounded close to this Polar Ocean Thermostat Set Point.
The Thermostat for Earth is in the Polar Ice and Water but the whole Earth is not regulated to that temperature. The Whole Earth is regulated to the temperature that keeps the polar oceans close to the set point. The Earth's heat storage is mostly in the oceans.
When too much heat is stored, it melts Polar Sea Ice and that turns on snowfall. When too little heat is stored, the Polar Oceans freeze over and that turns off the snowfall.
If you understand a process, you can put a thermostat anywhere in the process, if it gives the results you want.
If you do not understand a process, but you have enough data, you can put your thermostat anywhere in the process, if it gives the results you want. The Polar Sea Ice Thermostat does not care what Earth Temperature averages. It just knows to turn cooling on when Polar Oceans are wet and it just knows to turn cooling off when Polar Oceans are dry. The rest of the process is complicated, but it always works perfectly. Look at Actual Data.
Regional Temperatures, all over the world, range above and below the Earth Average by huge values. Where else would you put a thermostat, other than in the Ocean? Oceans are the most stable indicator of Earth Temperature. Ice core data is mostly a measure of ocean temperature and we have the records from Greenland and from the Antarctic that shows these wonderfully bounded cycles.