From experience using TL 700s in the winter and spring which have just gone, it always felt to me that the heating has been on far dodgier ground than the air cooling has ever been.
Frankly it was always rare for me to find a 700 which was consistently heated to a comfortable level, if at all. I had a number of uncomfortable overnight journeys on cold and clammy 700s. At least a lack of heating doesn't matter on overnight services at the moment, but in January it is most unpleasant.
On the other hand, I tend to find that most of the cooling functions of the air conditioning work OK. First Class does indeed always seem to be at a different temperature, but this is no different to various other units of a completely different manufacturer and vintage - 171s are notorious for First Class being the only part of the train with working air con!