I'd be inclined to ditch the heatlamp, and have the thermostat probe between the heatmat and the bottom of the viv (with heatmat outside, under the viv, controlled by the thermostat. Hatchling corns are real escape artistes, and excellent at getting out through small holes!) Have the thermometer inside, with it's probe directly on the glass over the heatmat.
I'd also hold off on feeding the corn until you know the temperatures are good, as a few days without food are better than risking a regurge.