Are you saying that the chip stays at room temperature when powered on?
Yes , many microcontrollers these days are very low power, so they don't heat themselves too much. E.g. microcontrollers from TI series MSP430 have a PN junction that is internally polarized, and the voltage drop is read by the ADC convertor included on the MSP chip. Once calibrated, is a good enough sensor to make a room thermomether. It can even sense the raise of the temperature when keeping the finger on the chip.
If you can open the multimeter, try it. Keep your finger on the chip.
- Is it hot? Probaly not.
- Does the temperature displayed by the multimeter increases when you keep a finger on the chip? Probably yes.
Anyway, it's nice to have a cold joint compensated thermocouple on your DMM, congrats!