Might optimize the setup with two thermistors, but if it works with just monitoring the heatsink, that would be easiest (rather than having to insert a sensor in the sample container, which it is preferable to keep sealed; also such sensors would need thorough cleaning between batches to prevent cross contamination from one sample to the next).
What ever kind of switch(es)/keypad needed to program the number of desired cycles for a given run (besides, obviously, a main power switch).
Haven't picked out a thermoelectric unit yet; I was planning on experimenting a bit, but think that considering our sample size, probably something around 20W. But they are available much larger; here is just one source:
and one of their 18W units:
http://www.customthermoelectric.com/tecs/pdf/12711-5L31-02CK_spec_sht.pdf
In any case, definitely a DC unit, which can be "reversed" (hot side and cool side flip) by reversing the polarity of the power supply. You'll note on the spec sheet that these units vary their power handling (the amount of heat they transfer) with the input voltage; that, instead of pulsing, would be a way of throttling, but I didn't know if achieving a voltage throttling (on a fairly high current draw) would be as easy to achieve with an Arduino controller as an intermittent on/off pulse of, say, fixed 12VDC.
Thankfully, the thermal masses of various samples will be similar. I'm sure some programming tweaks would need to be done, especially as far as the ramping of the power to the thermoelectric unit (to not overshoot the maximum temperature) and the hold times at the freeze and thaw set points. Also thankfully, the unit will be run in a lab with a constant ambient temp; at least that won't be a variable. Once it is calibrated via a few test runs, where the actual freezing and thawing are monitored, I'd think it would be good to go.