I had a similar experience after buying a black lemon E36 coupe,
except some fella had put miracle head gasket sealant into the coolant and the problem only came to light after I changed the coolant, then all hell broke loose, flying temp gauge, blown hoses and a cooked motor, in the pissing rain on my way home from work....
had the car 2 weeks, cost me 4000 euro initially, rebuilt motor 1000....
It can happen to the best of us... no matter how much it sucks..
At least the car didn't cost to much !
you may just have a thermostat prob, but to be honest imo, I agree with previous posts saying suspect head gasket, a compression test may tell you the suspect bore, or have the coolant water checked with a test kit to confirm the head gasket...
a similar bottle of stuff may get you out of a fix !
some are guaranteed 99% of the time to repair the head gasket.
I am not recommending the stuff personally but it may help, and get you by for a few weeks while you save up..
best of luck with your sick cat, hope you get her sorted..