So Lissa called the service people again today to use the 30 day service warranty they gave us. They were able to come out this afternoon, and the unlike last time, the unit was still malfunctioning when they got here. The service guy was able to determine that a switch on the outside unit that's apparently supposed to automatically turn it off if it gets too hot was stuck in the off position.
To remedy this problem, he simply removed the switch and hardwired the connection. He said a replacement switch would be $150-200, but that he might not bother replacing it. He said the life expectency of a heat pump is about 10-15 years and that ours is 8. So rather than sinking money into a somewhat costly but non-critical repair, just save the money toward a new unit at some point. He left the decision up to us. That seemed reasonable.
There was no charge for today's visit and he actually advised us on a way to *not* spend money unnecessarily. I am pleased. This has been a far better experience than what we had with a different company when we had problems last year. Last year, repairs were delayed by problems with ordering parts. We had to live in a hot house for over a week. They gave us estimates at a couple points, but each time they did work ended up charging us substantially more. As a result, I called someone different this year.