Depending on how small the pet shop small rat is.
One week my pet shop small rat is not a lot bigger than a mouse, the next week they are 5 times the size of a mouse.
If the heat lamp causes him to abandon the hide, your best bet is to switch to under tank heat. Get a UTH pad and thermostat, and put it under his tank on the side with his hide, and use the temperature probe to set the thermostat to keep the temps on the glass at around 92 - 94. This will also help him digest his new bigger meals better.
Gale