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That said a TEC should have considerable thermal mass so you shouldn't need to switch that fast. A few options are writing a subroutine with a series of delays, or using one of the pulse width modulators with a really slow clock cycle which can always be slowed down further by counting in a loop i.e. if (counter > 500) {change output and reset counter} else counter++; That can get you down to really slow frequencies
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I might get hold of a Teensy 3.0 to analog write the pwm frequency for my next project. In the meantime I'll look at a sub routine, as suggested and change pwm pin to 3 - 1khz instead of 3khz. Teensy's are intended to be programmed directly with C++. I am slowly working through the tutorials.
Timer libraries
http://www.pjrc.com/teensy/td_libs_TimerOne.html
Soft PWM
http://www.pjrc.com/teensy/td_libs_SoftPWM.html
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Looking at your circuit though you're running a MOSFET with 5V at the gate and 12V at the drain. To switch it on fully you need to be selective of your MOSFET. It could be you're never actually saturating the MOSFET if the Vgs threshold voltage of your chosen MOSFET is too high. This may cause a lot of heating. In your circuit for instance an IRF510 would dissipate 3W average, and an IRF1405 0.5W. You can verify this is happening by putting 5V at the gate (continuously) and measuring the voltage from Drain to Source. If it's not effective zero then you're not saturating the MOSFET and you're losing power across it. That MOSFET should not need a heatsink
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The freetronics smd mosfet runs a little warmer than the IRF2804 I have, although freetronics advertise it as logic level Vgs 4.5v - I think the rds on is not as low as the IRF. The heatsink is a precaution more than being absolutely necessary. I will try the saturation test on all the MOSFETS I have lying around.