Quick experiment here: a proof-of-concept of a thermochromic display. This is about as simple as it gets: a short length of nichrome wire underneath a thermochromic liquid crystal sheet. Putting a small current through the nichrome heats the wire and causes the liquid crystal sheet above to change color.

I used the liquid crystal sheet from American Science and Surplus (part number 91582P1) as well as this nichrome wire from Amazon. (Recently, nichrome wire has become surprisingly cheap and widely available because it serves as the heating element in e-cigarettes.)

I soldered about an inch of the nichrome wire to a protoboard. Solder does not wet the nichrome well so I made small loops at each end for a good mechanical joint to serve as an electrical connection. Some double-stick tape helped make a good thermal connection between the nichrome and the back of the LCD sheet.

I used an Arduino to PWM one channel of a ULN2803A Darlington driver, enabling the PWM on and off at about 1Hz. I connected the nichrome wire between +5VDC and the Darlington switch to ground, and carefully increased the PWM value from zero until I could see an effect. Some care is warranted here: the resistance of the nichrome wire is only about 2 ohms so turning the driver on fully could draw enough power to either blow it up, burn up the nichrome, or both.

Obviously this is not particularly practical: it's likely fairly sensitive to ambient temperature, and naturally won't work if too hot or cold, but I was pleased that the thermal mass was low enough it could change state quickly enough to be useful for an information display of some sort.

This is a proof-of-concept of one segment of a seven-segment display. Obviously the next step is to build a clock using four or more seven-segment thermochromic displays. In the fine tradition of geek clocks, it would be temperamental and inefficient and might not actually work that well, but hey: geek clock. (I would probably start with this neat 1-inch design for the Micro Word Clock, here's hoping I have some more time to fool with it.)

Update 2020:

Someone actually built a thermochromic display, saving me the hassle of doing it myself! It looks a little overengineered: I would have used a heatsink rather than Peltier Junctions, but they do them!