2000 beetle blowing HOT air out vents

[lmnreed]

2000 beetle had AC check, but we have a blown compressor. Had red temp light go on a few times in May 07, but hasn't come on since. Husband changed the thermostat, checked fuses on panel and above battery. Flushed radiator and refilled. My question and what I'm worried about is there is very hot air blowing out of inside vents. It doesn't matter if the dial is turned to cold or hot. Even on very cool days and nights it is still hot air. I've noticed lately that the fan hasn't been on when I stop the car. But I also touch the hood and it is never hot????? I've listed all the chats on water pump to sensors for husband to check. Another odd question is the temp gauge inside the car will read a lot higher than what the air is outside. Example the other day it was around 90 degrees and my temp reading in the car said 114???? Any suggestions are greatly appreciated! Thanks!