Testosterone was the standard of care for men with depression before all those oral antidepressants were available. So it definitely helps with the happier person part.
If I had to guess, testosterone also cranks-up your metabolism via increased activity of your anabolic pathways. Testosterone is mother nature's signal that conditions (food availability, sleep conditions, environmental stress, etc. etc.) are good and we should take on muscle, hence we'd naturally be less efficient with food. Costisol is mother nature's signal that conditions are tough and we should lose muscle mass and store fat thus becoming more efficient with food.
So I'd speculate that testosterone doesn't necessarily make you warmer -- but it does crank-up your metabolism because your body doesn't see the need to burn food at its highest efficiency.