Kymasabe

SO, my new-to-me 92 F150 temp gauge hasn't been working right, or maybe it has, I don't know. I just reads low all the time, never really gets into the "normal" range. I figured it had a bad temp sending unit and just read low all the time. Only time it did read higher was when my brand new serp belt tensioner failed 10 minutes after install and ate my serp belt, truck ran hot as I limped it the last couple of miles home and gauge read in the middle of the normal range while it started spewing coolant everywhere. Otherwise, always reads low.
So, last weekend I put on new radiator hoses, flushed the system, fresh coolant, new radiator cap, did some small drives with no problems. Today it took it for some longer drives running errands and the temp gauge started reading higher than it usually does, got in the low end of the "normal" on the gauge, needle on the N or O and I was starting to worry it was running hot. But, not a single drop from the engine area, still coolant in the bottle, no leaks. The question is...is it possible that flushing the cooling system and replacing with clean fluid could possibly affect the temp sending unit and make it start working better again? Or is it more likely that I have a bad sending unit and the truck is indeed running hot and I have a cooling system problem?