Challenging application. Do you really need max 1500C? You mention the piece reaches temp at 800C. What kind of accuracy? Precision?
A K thermocouple (if only you could use one) could get you +- 10 degrees, +- 4 if you carefully calibrate the system. I can't think of any DIY non-contact solution that could come anywhere close to that.
If ballpark temperature is good enough, then - use a camera: the colour of the metal tells you the temperature. The metal will radiate in the visible spectrum above about 600 degrees, and the colour will shift from deep red to yellow/white by about 1300. At 800 it will be cherry red. In other words, use a camera to estimate the temperature the same way blacksmiths have done for centuries. Of course you need serious IR (heat) filtering and your temp estimate will be very ballpark.
One big improvement would be to use a spectrometer - which you can make yourself (for example see instructions here. Also noodle around on the publiclab.org website - it's a great resource). Just replace the webcam with a camera module you can connect to your hardware.