Yes, it is a thermal ballast resistor. The internal heating when running is what causes it to increase cold resistance from cold to hot. Cold means around 25 or 30C.
One test you could run is to use a wire jumper while it is running and hot and the irregular idle is occurring. Just use the jumper to short the low resistance terminals of the ballast and see if that improves the idle quality. While you are in the garage, measure the primary resistance of the coil + to coil - as suggested, with all wires disconnected. It ought to be 1.5 ohms + or -.
BTW, this looks like a replacement ballast resistor. Some of them are not true OEM replacements.
