I am going to have to replace the attic fan (probably). The inspector said it would not come on and yesterday I realized I need it when I stuck my head in the attic and felt 120F+ temps. It was maybe 78F in the house and 85F outside.

So what I am looking for is a fan with a thermostat that I can control from in the house that reads the temp like my heat/ac thermostat does. I'd like to maybe set it to come on at certain times and be able to turn it off when I am away. Is there anything like that available? The attic is maybe 1000-1200 sqft.

I was looking at this model (Ventamatic CX1500 Power Gable Ventilator Fan):

 

The one you posted operates off temperature variances, but you can wire it to a timer ahead of the thermostat and it will only work on "time" and "temperature", with time being primary. If you have it set to 1pm for an hour and it is 35 degrees outside, it won't come on.
I don't like attic fans. They are a failure waiting to happen, as you have already seen. Proper soffit vents and ridge vents will move more air, more completely, and are passive.