Why does the Heat/AC work intermittently?

What is your question?

The heat and the AC work intermittently on my 2002 Prius with 245 K miles. The radiator was just flushed and a new thermostat was installed 2 weeks ago. After this, the heater didn't work at all on a very cold day (3° F) and did finally work after running about 15 minutes the next day (15° F). Last summer the AC was working in a similar manner. It would kick in and out. Have not been able to test the AC after the flush and replacement. Any suggestions to look at next?