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Could I get something like this, a 12v silicone heating pad, and vary its temperature with an arduino somehow?

http://www.banggood.com/Waterproof-Silicone-Flexible-Heating-Pad-6060MM-DC-12V-10W-p-972464.html

My grand plan is to put temperature sensors on it and make it hit a certain temperature, and make it hotter/cooler to try and reach a target temperature.

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In principle, I don't see any problems. Your heating pad uses 12V and 10W, which means it would be consuming slightly less than one amp of current. The MOSFET you linked can go up to 5A (needing a heat sink with over 1A).

You could use PWM (there are 6 pins on a Uno that can do that) to provide pulse-width modulation to control the amount of output you give to the heater.

You would, of course, need to measure the heat of the device to work out when to adjust the PWM output. You might look up using a PID algorithm to adjust the PWM output depending on the sensed heat input.


References:

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If you want to control the temperature very accurately, try connecting a shunt resistor (value: <0.1 ohm) in series with the heater. Use an op-amp to amplify the voltage difference on its two terminals and read with Arduino the resulting value. You can calculate with it the actual current and therefore the actual resistance of the heating pad.

The value changes with temperature, you can use the resistance value to measure the surface temperature of the heating pad.

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