Rolled off the lot today, engine problems.

Rolled off the lot today, engine problems within an hour

I bought a used 2004 Chevy Impala today, using $5,300 of my hard-earned money (I am a college-student). 123,000 miles. Reputable Subaru dealer, CT. I “Kicked the tires”... Test drove it, checked CarFax, inquired about any repairs/inspections and the status of the vehicle. Check engine light was on. They looked, it was the thermostat. They replaced, detail, oil changed, ready to go. I know it’s “As Is.”

I live an hour and 30 away from the dealership. After just over an hour, I noticed “Coolant temp high” lighting up in red. Luckily we were almost at our destination. We both pull over at an abandoned gas station. The temperature gauge was almost on red. I could not believe it. We pull over, and check the coolant... The coolant tank contains fluid, and appears to be full. We leave it where it’s at, drove his car to the auto parts store and picked up some coolant fluid. We returned about 45 minutes later. The coolant fluid had pretty much leaked out. We refilled it, and got it back on the road. We drove to two places, then to my dorm, and the coolant was still in when we checked again this time (we only drove rather short distances, no more than 10 minutes total).

At this point (as of 30 minutes ago, the last time I parked it), the temperature gauge is showing problems. It’s abnormal for a car to ever go above halfway up on its temperature gauge, yet this keeps doing this. The heat inside of the vehicle is not working properly. What will happen is the heat will be on full blast, yet no heat actually comes out. But as the car is moving, heat will begin to come out of the vents and I’ll notice the temperature gauge dropping to below the halfway point. As it’s parked, I’ll notice the temperature gauge rising. This seems to indicate a problem with the thermostat.

I feel like I just plunked $6,100 (after taxes and other docs) down the drain. It could be one or more of a number of things... Radiator, thermostat, water pump... God knows. I drove it away and this happens AN HOUR LATER. Please, someone, let me know if you think there is any hope for this vehicle and what you think the likely problem is (and how much potential repairs may be).