Do you know if thermocouples are "qualified" according to their precision?
not cheapies on ebay .

a more likely source of some probes with actual specs would be rs components ,farnel/element14 ,digikey or similar
but they will cost more.

I have never had the need for real absolute accuracy and just add or subtract a suitable offset to compensate for error,
so far it works acceptably for my 3d printer [precision being more important]