Did they think that it was possible to come up with purely objective measurements of "hot" and "cold" material? What are some sources I can use to learn more about the history of thermodynamics?
Bonus question: did the European understanding of temperature measurement conflict with the understanding of temperature measurement in other areas of the globe (eg. China?)
I don't have an answer for periods as early as that, but for the development of modern thermometers in Europe (17th century and onward) and their relationship to the history of thermodynamics, see Hasok Chang, Inventing Temperature: Measurement and Scientific Progress.