Problem is that you will get a 2-3 degree differential with that thermostat. I know - I use them for my adult racks (I'm cheap). A 4 to 6 degree variance in temp will probably kill eggs.
I'm using the same type of incubator, using a marine cooler. I'm using a herpstat and my temps flexuate .5 to 1 degree from side to side.
The thermostat is the most important thing - buy a good one.....