This was just off the top of my head, but I imagined the thin rods having low enough thermal mass that the active TEC cooling would not cause fingers to significantly heat up the rods.

That is, the TEC cooler should be able to relatively quickly lower the temperature after the finger is removed.

Again, off the top of my head idea so no idea if it would work or not, but doing a quick viability check should be relatively easy and cheap.