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Hi Jacob,
What are the actual temperatures involved ?
Can you be more specific about the final application. Thermal-ballistics are going to affect time constants etc.
Regards,
Mark
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Similar projects have been done many times using an Arduino as the controller. Google “arduino temperature control” or “arduino heater control” for lots of ideas.
Also look up “Proportional Controller”
So you have two thermometers (Sparkfun sell digital devices like the DS18B20).
Setpoint for your control loop is +3 degrees (difference between the internal and external sensor)
And the controlled element is the external heater, possibly using PWM.
In very basic terms heater_pwm = (((ext_temp - int_temp) - 3_degrees) * loop_gain)
Simulate (using a spreadsheet ?) plug in numbers and see what happens - make sure its does what you want before you build it.
One of the issues you have is that if the external box gets overheated, you don’t have any cooling mechanism available to compensate.
External overheating can be due to having applied to much electrical heat, solar heating, or some other unexpected mechanism.
You may want to add an alarm if the temp difference gets to large.
Is this a commercial or university project ?
-Mark