You want to measure the temps inside so placing it exposed to the inside of the cooler is better, also place bottles of water on top of your heating source, this helps to hold temps even and stable, if there's a loss of power your temps should hold for a bit.
Awesome, Thanks. I just put the thermostat probe on the outside of the heat tape. I was thinking of using some of the larger ice/heat packs with the blue gel for the same purpose of the water bottles. Thanks for the tips and the link.