In Shemirath Shabbath by Rav Yehoshua Y. Neuwirth, 40:2:
This chapter talks about medical procedures on shabbos.
The Halacha starts by saying
a. 1) It is permitted to measure body temperature on Shabbath.
f. 1) Whether or not one may use a forehead thermometer (consisting of a strip of celluloid which changes color, according to the temperature, when held in contact with the forehead) depend on its type.
2) It may be used
a) if the temperature is read from a change of color alone, and form of letter, digit or other symbol appears, or
b) if the temperature is read by means of letters, digits or others symbols which are visible before use, but change color or become more pronounced when the thermometer is placed in contact with the forehead.
3) If the letters, digits or other symbols by which the temperature is read are not visible before use, the thermometer may not be used.
There may be a leniency here because of a sick person, I don't know. But it's certainly clear that if the writing in the cup is not visible before heating, it's certainly prohibited.
Assuming there is no leniency (and I don't think one is being used since there are no qualifyers in
a. 1, but of course I can not rule on this), then a change of color in the cup would be permitted, and making letters change color is also permitted, as long as they were visible before hand.