Exhaust Repair 01 Cavalier?

My muffler fell off the end of my car by the clamp that holds the pipe from the manifold. It was rusted in that area only. So I cut the pipe and used a adapter to go into the muffler and also fit the existing pipe which is still pretty good. Once and a while my tempture gauge goes up and down but the car does not seem to overheat. I just did this job this weekend. I checked the fluids under hood they are ok. Is it related to this adapter, the tempture gauge going up and down. It usually does this when I Idle in traffic. The cars runs good. No crazy loud muffler sound at all. Has anyone experienced this problem before? Any thoughts at all would be appreciated. Thanks in advance.