Constant Power Micro Load
The type of PTC you need is a ceramic one, I don't think the polymer "polyfuse" type are suitable. PTC ceramics were commonly used as fairly constant temperature heaters, and probably still are in hair-tongs etc, where they use a PTC thick film resistor printed on a ceramic plate.
However these are commonl;y used today for pretty high temperatures, which might be more than you would want inside a soft plastic connector.
If you use overcurrent protectors, you will also find that these are high temperature devices - they will have to idle at (say) 120C. If you use an SMD device. this means the soldered joints and pcb have to take that, which they might not like long term. Against that, this is not really a very high value or very long term device so it might not matter. Leaded disc types transfer much less power to the pcb and solder, so would be a more reliable choice. There are PTCs for sensing with s lower slope, and which have a much more constant slope rising from lower temperatures.

Motor protection PTC's have much more that range you are looking for. When you look at the lower sense temps (50-90C e.g. B59100M1070A070) you will see that the don't have the nasty NTC part at the start of the curve.



FYI, here is a constant power, constant current circuit. This also meets your objective using very cheap components, and without requiring a very specific thermistor.

The constant current emitter follower Q2, has its reference voltage subtracted by the current mirror Q1Q3 in proportion to the supply voltage. The result is a linear dropping current i.e. constant power when the slopes are balanced. R3 is the primary slope adjuster.







simulate this circuit &ndash; Schematic created using CircuitLab

We can simplify this using Q4 to replace the zener (Q3 cancels Q2 VBE, so Q4 provides the constant reference voltage). This gives an NTC, but this is what we want. 2 dual-npn and 3 resistors is about as cheap as you can get.







simulate this circuit

Flipping the circuit around we can gate it with a TL431 to control stop voltage, and give near zero off current







simulate this circuit