Here's the backside, just battery leads.
I desoldered the heater and charging contacts from the board and removed it to inspect the heater.
Removing the insulation reveals the oven. The oven is heated by the serpentine traces laminated in heat resistant plastic tape. The temperature sensor is a surface mounted thermistor that is grounded on one side with the other side connecting to the board. It most likely forms a voltage divider with another resistor on the board to supply a temperature-dependent voltage that the microcontroller can sample. The thermistor tested good with a multimeter.
Here's the locking mechanism that is used to change the position of the mouthpiece.
After verifying that the heater was working by testing it with a voltage from my power supply, I traced the heater wires to a transistor on the circuit board that drives them. I could barely make out a mark on the tiny SMD chip so I looked at it again with a microscope.
At this point I was pretty sure that I had found the issue. You can tell this chip is burned out from that mark on it. Also that solder bead looked pretty suspicious. This chip was definitely getting hot.
Since I already had the microscope out, heres a close up of the RGB LED used as an indicator. You can see the individual cathodes for each color.
I ordered two new transistors to be safe. If you want one, you can buy this part
Old chip removed
Solder paste and new chip
New chip soldered in place
Cleaned up all the flux
All put back together. It heats up!
It charges! I was unsure if it would be repairable when I first opened it so I was very happy to be able to fix this one.