For C210 the heater current seems to flow through the thermocouple and for C245 the heater can be powered separately.
The C210 schematic is from Xyphro's Nanosolder.
C245 pinout:
I've been fooling around with my JBC station (the cheapie BT-2BWA) looking at how I might make an add-on box to autoswitch between the T210 and T245 irons I have (you can actually buy one but I already feel bad enough about buying the station instead of DIYing it), and have made some notes on the way it works and how the tips are wired that may be of interest:
First of all I can confirm the quoted diagram is accurate - you can measure the thermocouple voltage between C1 and C3 (otherwise a dead short) and the heater between C2 and either of the other connections (with C3 showing the TC voltage in series also). This is despite some images of actual JBC tips being ground down suggesting otherwise (possibly due to them being older 2245 series tips, though I have one of those too and it also matches the diagram!).
The C210 tip on the other hand has the same connections as shown for C2 and C3, but C1 is a dead short with no TC voltage to C2. I assume this is for physical construction reasons - these things are tiny!
The station itself uses C2 as it's internal common ground connection (via a current shunt), and applies the AC heater voltage via phase angle control between this pin and C3. The full heater current flows via the thermocouple in both C210 and C245 cartridges! C1 is only used for sensing and there is no substantial current path possible (other than to mains earth, to which it is hard bonded in this station).
Heater current is sensed by a 0.05R shunt, rectified by an op-amp based ideal diode bridge and then amplified before going into an ADC. The station will reject any cartridge with more than ~10-20% lower resistance than expected (didn't test properly with higher).
TC voltage sense is done between C3 and C1 using a OP07 precision op-amp at a gain of -370 (appropriate for the 5V micro used - 3V3 based stations use more like x245 gain). There is clamping on the output (opamp is running on dual rails outside the microcontroller ones) but I can't see anything other than 4k7/2k7 resistors protecting the input from the heater voltage, which seems a bit rough on both the opamp and the 0805 resistors (assuming there is some clamping to supply rails going on inside the OP07).
There is also a 100x gain OP07 amplifier between C3 and ground (i.e. effectively C3), again going to an ADC input - this saturates during heating operation and I haven't worked out exactly what it is used for.
There is some other sensing stuff going on with C3 and C1 - C1 has 1M ohms to 9VAC, C1 has 100k to ground and between them there are some more high value resistors and a multi-transistor circuit I couldn't be bothered tracing heading off to a digital I/O pin.
Finally there is some zero crossing detection stuff and inputs for tip-change, sleep and T210 detection (all with 10k pullup to +5V and 10k in series with the GPIO input).
Hope these rambling notes make some sense and are of use confirming how JBC themselves do things (also see a much better effort, albeit with possibly incorrect cartridge diagram, here:
https://www.eevblog.com/forum/testgear/jbc-soldering-station-cd-2bc-complete-schematic-analysis/ )
Edit: maybe the C245 cartridge can be wired in a couple of different ways - series and separate TC depending on where the heater wire terminates. I don't think it would make a big difference in operation and would explain the tip teardown I saw and some notes on the Unisolder project saying "series or separate TC".
I will also join those expressing interest in the OP's implementation of the ITBH algorithm - I need to build a Weller micro-tweezer controller and working out a control algorithm that deals well with the small-mass tips is one of the things I have to look at.