Fuel gauge

Hey this winter I started having a problem with my fuel gauge. Upon startup of the engine the fuel gauge is slow to react. Eventually it builds itself up to the correct fuel but it takes time. Sometimes miles of driving until the needle catches up to where it should be. Ironically about the same time this happened my heater started acting funny. I do not know if these are related. By acting funny I mean I would start up the car and the car would start warming up. Just about the time the temp needle gets to full hot temp, the heat drops out, the vents start blowing cold air for about 30 seconds then it switches back over to hot air again. I am not really worried about that at this point in time but I am wondering if there is a relation. Any help is appreciated. I am really concerned about the fuel gauge because its driving me nuts. Thanks

Hey, hows it going? Can we get a little more info on the car before we get going? ie-year, notor, fuel system, yadda-yadda? That would be a great help to find you an answer.

I am sorry -
2001 Trans Am
5.7 Liter
Nothing special - no upgrades
105000 miles
Any other questions - just ask

Try checking fuses first just to be safe. I had a problem with acuall gage cluster on a 91 iroc, it only effected the speedo so it could have an intermitent connection or it could be your sending unit in the tank taking a dump on you. I'm sure someone with more insite on fuel systems will chime in. I'm geussing its the sending unit in the gas tank that is the problem.