You sound as though you're up for a bit of a project.
Here's what I'd do.
Look at the LM35 series of temperature transducers on the DigiKey site. They are easy to implement because they output a voltage that can be directly read as a temperature with a cheap DVM. Wire length, gauge, and type can be ignored.
IIRC they are available in degrees F, C, or even K.
Make sure the one you pick will measure your max temperature.
There may be a more convenient location than the drain plug.
I would be leery of immersing the sensor in the oil, even if potted and shrouded. I'm thinking that you'll get the information you want simply by gluing it to the casing with thermal transfer in mind of course.
Thermocouples, thermistors, and RTDs require an awful lot more effort.
So far, everything that has surprised me has been completely unexpected.