2004 Pontiac Grand Prix overheating

I have already replaced the thermostat and it seems to overheat as soon as the car is cranked. I have read the article and my passenger floor boards are wet and it seems to be coming from behind the glove box but it has been rainy in my area and I assumed it was from the rain. I do have to press the gas to start my car as well and when im driving the panel has said lowered power level but once speed picks up the warning disappears. I have been putting water in the reservoir and there doesn't seem to be a leak from underneath. I don't know if it could be related to this issue but my ac only works when driving at high speeds as well if I'm not pressing the accelerator it will not blow, I have my uncle looking at it but he doesn't know too much himself is there any way u can help me pinpoint what is going on with my vehicle