Firstly, You might notice that there are two different Table 4's in each of your sources. One has its third column as C/T current (as pictured in your answer) and one as voltage (as in the document). I'm going to assume this is actually a voltage because of how it increases with resistance but double-check this. I would guess this is a good old-fashioned potential divider controlling the compressor speed.
If 7 is a thermostat connected across C and T, I'm again assuming, this will probably be a simple bimetallic strip (or similar) that's just going to make or break the circuit.
The second thing to figure out would be how the voltages at C at T connect to the rest of the device (if at all). Ideally, I'd hope that T is connected to the negative voltage, but it might be isolated, or something else entirely. It will be important to make sure you've got a good handle on your negative voltages in something like this.
There's then a few options depending on how much granularity you want. You could use something like this circuit
simulate this circuit – Schematic created using CircuitLab
Below gives you a range of 130 Ω - 1.5 kΩ. You can fuss about with the exact values depending on how many settings you feel you need, and what exact range you'd like, you can of course include 0 Ω. This is good because it's simple, and has a relatively low part/pin count, but it's non-linear and might be a pain to code if you need a control loop. This is also pretty similar to a relay-fixed resistor approach suggested by danmcb.
Alternatively, if you have some kind of DAC you could use something like
simulate this circuit
[edit] I've added a voltage source to act as the DAC, and a voltage source + 800 Ω to act as the CT source. [/edit]
You can aproximate a dac using PWM and filters, which would probably suffice for this (I assume). This circuit works basically by specifying the voltage at C, and the op-amp/MOSFET sort themselves out. I note you're concerned about the heating in a MOSFET, but the actual power dissipated is going to be 10 mW, so not really anything to worry about. If you go down this route, be sure to check the MOSFET voltages work. It might be hard to find a MOSFET that's happy with a very low VDS. I've popped a series resistor in there, but the value is arbitrary, again I'd check/simulate this. You'd have to remove it if you wanted to get close to 0 Ω for the lowest speeds. The advantage of using an opamp is also that it will compensate for any drift.
It's worth noting the op-amp has positive feedback and therefore could oscillate or ring if not damped properly.
I'm sure there are other ways, but these are the first two I can think of. I've made a lot of assumptions, that I don't think are particularly silly, but do double-check them.