OOPS ..... i'm sorry, i'm so used to chat with friends that have basically my same hobbies (mainly electronics), that always tend to suppose that anyone already know what i'm saying ..... my guilty, apologise.
Here is a basical schematic that i use in some applications with small TECs for regulate the temperature ..... it's a 12V version, and it's optimized for my specific use, so maybe you need to try to change some values a bit, but it's a good and stable enough base for start to experiment (well, if the inventors of the NE555 see my schematics, probably they want to kill, me, but hey, they works, so .....
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Sorry, i drawed it in hurry, i'm going home, so it's not too much elegant, but i think it's easy to understand ..... use 470uF/25V and 100nF ceramic on the power supply line (i not drawed them, but is an usual filtering value) ..... the mosfet i'm using are IRFZ serie, you can use any with similar characteristics, and that hold the current needed for your TEC.
Basically it's just a low frequency (from half second to 2 / 3 seconds, depend from the temperature of the NTC) pulsed driver with a big difference in variation between the ON and the OFF times of the cycle ..... the NTC is a common miniature element, with 10 Kohm value at 25 C, but you can use different ones, i use these ones just cause are the more easy to find around here ..... it switch on and off for short periods (approx half second) the TEC, and when the temperature drop, it just elongate the pauses between the pulses, til it stabilize ..... and when the temp rise again, it short the pauses, giving more power to the TEC.
If you have a fixed voltage TEC, you can just attack it directly to the circuit (as example, TECs built for regular use at 12V, can work without regulation, with the circuit powered at 12V) ..... if you have TECs with different voltages, or you give a different power line to the TEC, or, better, just use this circuit for power up a voltage regulator that can feed enough current to the TEC (like, if you have a TEC rated for 5V 2A, you can use the circuit for feed a voltage regulator that then give the 5V 2A to the TEC)