Kevin and I set up a measurement for the heater in the lab. I have attached some pictures of the setup. The power comes from a 24V voltage supply which will later be swapped for a 24V cable. We connected the DAC to the circuit and set the voltage to 0.8V. To connect up the heater, we had to use a terminal block to connect the wires from the heater to the wires of the Lemo connector. We will eventually attach the wires of the heater to a Lemo connector as well to avoid having to do this. We attached the temperature sensors using a breakout board, since the connectors weren't the same. I'll be building a box later today to be able to connect it without using a breakout board. Also, when connecting the DAC to the circuit, I made a D9 to BNC connector, but I wired the ground and signal backwards, so we also needed a polarity changer to attach it correctly to the DAC channel. I will fix this today as well.
We measured the temperature of this setup using one of the sensors for a few hours, then turned off the voltage and let it cool down again. Kevin made plots with the data. I then calculated the approximate time constants for heating and cooling. For heating, it was about 1.67hr, and for cooling it was about 2.22hr. Since we didn't reach the asymptotic value completely, I assumed the maximum value it could reach was about 29C.
Edit: attached photos of the setup and Kevin's plots