Yes, this absolutely possible.
Below I am going to summarize the proposed solutions with their associated problems and propose one idea of my own.
Solution 1: pyrometer has been proposed by Andy aka and mentioned by Olin Lathrop. The associated problem is sticky dirt blocking optical tract.
Solution 2: copper wires have been proposed by Olin Lathrop. The associated problem is much wear and tear on the wires.
Solution 3: transformer/coil has been mentioned by Olin Lathrop. This can be used with a thermistor, or you can see if your valve has a useful slope of its magnetic characteristics in the region you intend to measure. I would prefer this approach, especially if it works with valve as the core and no other stuff. Maybe Olin will explain associated problems.
Solution 4: something like an RFID sensor chip. The associated problem is the need of custom high-temperature sensor chip made of gallium nitride or some other temperature-resistant semiconductor material. A major engine manufacturer can very well order such a chip, but you will certainly need professional consulting. Also, I'll mention here that there is a lot of alternative options to power the RFID chip in the walve, including possibly piesoelectric or thermoelectric generation, so the power does not need to be transferred wirelessly, only the signal.
Note that first two solutions attempt to solve the original problem, not building of an LC circuit.