Interesting situation, because it is opening the cold water valve even when the setting is on hot.

I think the problem is either in the timer or the temp selection switch, and I lean towards the temp selection switch being stuck on a cold water setting.

GE allow almost no documentation to the outside, so you are going to have to look inside the console and see if a wiring diagram is present. If so, see if it will allow you to test continuity on various settings on the temp selection switch.

At the end of the day you may just have to replace it to confirm the problem, butr see if you can do some testing first.