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You can use relays as you originally proposed or a H-Bridge, the really critical consideration is the thermal mass you are controlling.  Peltiers are generally fairly large and usually thermally bonded to something, perhaps a container for whatever you need to keep at set temperature. It therefore makes little sense to think in terms of microsecond pulses of current, you may need seconds or even minutes of power being applied for the temperature to change significantly. For that, if you want to experiment and keep things simple, you can use relay control and just on/off full power. Shorter periods mean less heat/cooling and longer periods for more heating/cooling.  The temperature will obviously ramp up or down to some degree but that's where the thermal mass will average it out.

If you go down the H-Bridge route you avoid using relays and that might improve reliability but at the expense of more complicated electronics. You can still use the same principle of using the bridge to turn power on and off and to reverse the polarity but when the mechanical limitations of a relay are removed, you can do it faster and hence reduce the ripple in temperature.

Both ways control the heating and cooling by applying full power but for a variable repeating period so the average effect is "power/time" rather than analog control of the current through the Peltier device. You can read more about this if you research PWM (pulse width modulation) which uses the same principle. In essence a switch turned off does not dissipate any power because nothing flows through it and a switch turned on only dissipates power from resistive losses in its contacts, almost nothing in both cases. In contrast an analog system works by having the capability to provide maximum power but diverting any unwanted excess as heat elsewhere.

Personally, if you want to use Arduino, I would go for the H-Bridge option and drive it with slow (a few hundred Hz at most) then use an analog input to sense the temperature, another analog input to read the temperature you want, or make it settable by some other communication method, then a simple PID routine to make the actual and set temperatures match each other. The output of the PID calculation would then set the PWM duty cycle.

Brian.