Here's a thought for dealing with two issues at once: saving on your heating bill and getting buff.
Next time when you feel cold and are about to turn that thermostat up, stop, drop and do some push ups! This technique will help you with your push up challenge. By no means should you limit yourself to push ups. Jumping jacks will certainly do the trick as will kicking out some burpees (aka squat thrusts). You could always do some ab work too. Or some lunges. You get the point.
Try it! I just did 20 push ups. Not only do I feel warmer, I feel revved up and energized too.
What do you do to stay warm? Share the details in the comment section below.