Yes, it should and it could give a temp readout. However, this is apparently what the computer does if it doesn't get to the desired temp in a set amount of time. It turns the temp display to read "---", turns the fans on high, and i think it may disable the a/c.
If you do a search, theres a couple threads on here. Here's one of them. There are a few threads that debate on what the problem is.
Like I said, I know for sure mine is the thermostat. Because, It can take a while to warm up sometimes. As soon as it would reach 160F, it goes to "---". So in my case, since I have access to a scan gauge to reset it, and the readout comes right back on without touching anything I know its not wiring or a sensor.