I am building a hotplate that uses a thermoelectric cooler. To adjust the temperature of it, I want to use a potentiometer to regulate voltage. I am having difficulty selecting the correct one.
the specs for the thermoelectric cooler are listed below. My power supply is 12VDC. Also, is the potentiometer the best way to do this.

• 40 x 40 x 3.6mm
• lmax - 7A
• Umax - 15.4V
• Qcmax - 62.2W
• Tmax - 69C
• 1.7 Ohm resistance
• 127 thermocouples
• Max Operating Temp: 180℃
• Min Operating Temp: -50℃

 

Your TEC will take about 5A at 12V = 60W.
If you choose a potentiometer it will have to handle as much current and power, 5A, 60W.
What you need is a variable power supply, not a potentiometer.

 

I am building a hotplate that uses a thermoelectric cooler. To adjust the temperature of it, I want to use a potentiometer to regulate voltage.

I don't quite understand why you are using a thermo electric cooler to control a hotplate.
If it is just a question of controlling the power to a resistive load to control the temperature, then the best method for 12V DC is a simple PWM controller

 

i am using a TEC because it is magnetic stirrer/hotplate. Can't use a "regular" heater because it will melt the fan with magnets on it that generates the magnetic field.

 

Just how hot do you expect the TEC to get?

 

Everything you want to know about TEC is here......

http://www.tetech.com/FAQ-Technical-Information.html#13