Now that I have read your question a few more times I think I got it.

The heat tape is going to get hotter than the desired inside temp. Try putting a computer fan (need a 12vDC power supply) inside at the bottom of the cooler to circulate the air. This will even out the temps all around. Place a digital thermometer where your eggs will be and makes sure the temps stay within a degree or two of your desired incubation temp. If those conditions are met and it holds humidity pretty well (which a cooler should, especially with some damp vermiculite for the eggs to sit in) you should be good to go. I am not familiar with that thermostat but assuming it is accurate enough to keep the temps stable and not create an overheat/under-heat pattern you will have a successful clutch.