I have a Peltier module that I was thinking of using to make a humidity sensor based on the dew point temperature. To do this requires mounting a smooth flat mirror on the cold side and then lowering the temperature until a light film of condensed moisture forms on the mirror. An IR LED reflects light off the mirror surface into a photodiode and thereby detects when the moisture forms. A feedback loop controls power to the Peltier cooler to maintain the temperature at the point where the moisture film just forms. This means a constant cycling of power because the film must be warm enough to evaporate and then cold enough to condense again for the control loop to work properly. A clean, dust-free, mirror surface is also required. Commercial versions tend to be a little pricey IMO, but the method can be quite accurate in measuring humidity and seems ideal for hobbyist implementation using an Arduino for control, data acquisition, and humidity display.
My point is this: you may not need to switch polarity back and forth from heating to cooling to accurately control the temperature of one surface. All you may need to do is control the power input, not reverse it. It is true that Peltier devices will pump heat in either direction, depending on polarity of the applied voltage, but they are significantly less efficient in moving heat to the cold side than the are in moving, and generating, heat on the hot side. In moving heat to the cold side, a Peltier device also generates heat that must be dissipated on the hot side. If all you are trying to do is maintain the cold side at a constant temperature below ambient temperature, then simply controlling power may be all you need to do.Turn the power input off, or lower it, and the cold side will begin to warm. Turn the power input on, or increase it, and the cold side will begin to get cooler.
Temperature control is never as easy as it looks. Things usually get hotter faster than they get cooler, which creates a non-linear and potentially unstable temperature control loop.
@Ewinci: Could you tell us exactly how you plan to deploy your Peltier device, the expected temperature difference between the cold and hot sides, the quantity of heat you need to move, and why you think it is necessary to operate the Peltier device as a heat pump in both directions?