Do you really need to know the actual resistance, or do you just need to know the relative position of the rheostat?
If the latter, then there's probably an easier way to get that info. Most circuits that use rheostats as controls or position sensors apply a current to the variable resistance, and measure the variation in voltage across the device. In many cases the current source is just a fixed resistor to a voltage rail.
I recommend a test. With the system in operation, put a voltmeter across the variable resistance and move it end to end, noting the voltage along the way. Can you use the voltage reading to give you the info you need? If so, you're done.
Note: This assumes that it's a safe, low voltage, and that the measurements can be made without exposing the technician (you) to bodily harm when making them.
Expanding upon MikeMI's comment.