I know you said you couldn't take you budgie to the vet but I would really suggest trying to find a way. It sounds like the leg is not healing in the correct way and could cause perching problems throughout your little guys life. If there is a real difference in temperature it could also be causing a problem in circulation through the broken leg due to pinched blood vessels, nerves etc in the broken leg. Some breaks will heal on their own but most will cause continued problems throughout the birds life. Sometimes the problems are minimal such as less ability to balance (which some people have to use specialized cages to help with) but some problems can be fatal. If you are unable to take the bird to the vet due to monetary reasons do you have a avian club/vet/sanctuary/rescue in your area that might be willing to let you surrender the bird so they can get it the help it needs? Some vets will even work out a payment plan with you if you talk to them in advance.
Are you positive the leg was broken and that there aren't any other underlying problems that might have caused this as well? Also the pinching or squeezing the leg is not a very reliable sign as many birds will "complain" if their leg is pinched and may not complain if their leg is just moved around or lightly squeezed. Did you actually see when and how her/his leg was injured to be sure what the cause was?