MaryAlana:
With the Peltiers you need to choose either heating or cooling but NOT both,
Normally, to cool one side you need to reduce the "heat" in the other side and more reduction, better cooling on the other side.
The Peltiers do not like "snap" On power, it should be incremental and in reality they are current devices for best life, so your controller should be a variable constant current source, indeed you may turn ON/OFF but the best is variable sources.
If compared to a gas refrigerator with the same electric power, the gas wins by several factors, like 6 to 9 times more cooling capacity per watt.
The circuit offered by another member needs a change to insure that the switching doe snot go ON/OFF continuously and it is done by adding a resistor to generate a hysteresis band, also to change the small transistors for MosFets or to replace the motor with N type mosfets and place the Peltier from + to the Drain of the added N Fet Drain.
If you want to use this type of circuit, let me know to make the additions, though we need to know the type of thermal resistor needed for your circuitry.
Nando