Does My Kenmore Ice Maker Have a Bad Thermostat?

I have a Kenmore side by side fridge, Mod.# 106.55603400. The ice maker quit moving at all. I replaced the timer module. Same problem. Someone told me if you pour water in and it cycles once, you have a bad thermostat on the tray. It made ice once and stopped. Does that mean it's the problem or can there be other reasons? I don't want to throw more money at it. Thanks.

By Mark from OH