tutorial/TemperatureUnits

There has been a recent change in the behaviour of temperature quantities in Mathematica. It was decided that it does not make much sense to add two celsius temperatures, or to multiply one by a coefficient. The moving average implies just those two steps:

MovingAverage[{Quantity[a, "DegreesCelsius"],
  Quantity[b, "DegreesCelsius"]}, 2]

and the result is expressed in Kelvins, for which the separate steps make sense. Try this:

Quantity[a, "DegreesCelsius"] + Quantity[b, "DegreesCelsius"]

Strangely enough, Mean is not affected:

Mean[{Quantity[a, "DegreesCelsius"],
  Quantity[b, "DegreesCelsius"]}]

In your specific case, I would suggest to reconvert the moving averages to Celsius.