My car had the same issue after I bought it. There were two options for me. The first option was to bypass the heater core completely. It's not really necessary in Hawaii because of our year round temperatures. The second option, which is what I went with, was to replace the heater core. I would've done it myself, but I wasn't confident in my ability to do so. I ended up taking it to a shop that did the job for $1,800. Didn't want to spend that kind of money, but wanted a permanent fix rather than a band aid. Don't know if it'll help, but just wanted to say a little about my own experience with cooling issues.