2005 Audi A4 05 A4 coolant leak

In December I bought a used Audi (2005 A4 turbo with 90,000 miles) for my 17 year old daughter. The following problems are making me crazy. Any advice would be greatly appreciated.
We bought the car with a Car Fax Report and a certified inspection blah blah blah. The day after purchase we took the car to an Audi repair shop where it came through a 127 point inspection with a suspension problem and a coolant leak problem that they "repaired". My daughter drove the car for about a month when simultaneously the coolant light came on and the temp needle redlines then immediately goes back down to half way between L and H. We took the car back to Audi where they replaced the water pump and timing belt (not cheap!) On the way home from Audi the coolant light came on and the needle did the spike thing again. Coolant level was a little below min in the reserve tank. After bringing it back to Audi and having the same thing happen another 3 or 4 times the Audi guy tells me that he doesn't know what the problem is but thinks its not a big deal!(Whatever!)
Another issue that may or may not be related is that the heater blows either crazy hot then slowly cools down when driving or ice cold when idling. Audi flushed the heater core which helped out a little but didn't fix the problem completely. They're now telling me to replace the heater core (again not cheap).
I've been driving the car for the past two days to troubleshoot before going back to Audi and flipping out. This is what's happening.
I drove around on day one. Aprox 40 miles, the coolant light did not go on but the level dropped from near max to just above min. On day two I filled coolant to halfway between min and max which is where it stayed for the first 30 miles. I then drove another 25 miles in the evening and the coolant light went on temp needle spiked and coolant level dropped to an inch below min.
This morning I checked for leaks and couldn't find any. I checked the oil and didn't see any abnormalities the exhaust is not white or thick and the car runs beautifully. I want to love it but it's making me crazy! I'm not shy to spend more money on it but I want it fixed.
One, paid for, "expert" online suggestion was that it may be a sticky thermostat and one suggestion from the local garage guys is that I have Audi do a "block check" on it to make sure there's no damage to the engine.
Sorry to ramble but I'm desperate to fix this problem.