One of the most common way is by measuring resistance of for example a meander resistor (meander to make it longer to increase the overall resistance R). There are many electrical configurations to measure the temperature-induced variations of the resistance. The resistor in MEMS can be made from a number of metals such as aluminium and molybdenum (both are CMOS process compatible), with molybdenum more preferred because of its higher resistivity. The resistor can be calibrated over a range of temperatures to make the measurements more precise. The temperature is deduced from the changes in the resistance.
Piezoelectric or piezoresistive type MEMS sensors use the cantilever or beam which gets strained due to thermal stress. Effectively the sensing element can sense the temperature and can output in terms of potential or resistance depending upon the type of the sensor.
To add on to previous answers, temperature is most commonly measured using a resistance temperature detector, or RTD. These are often composed of serpentine metal traces with a known resistance coefficient (platinum is a common choice). When the temperature of a metal increases, the resistance increases. Another method can use a semiconductor material such as polysilicon or germanium, or a semiconductor junction, which can have a much larger temperature coefficient than metal RTDs. Some of my research has actually involved using microfabricated electrodes to measure the temperature in fluids, by measuring the change in ionic mobility with temperature: check out Article An Electrochemical Impedance-Based Thermal Flow Sensor for P...
Hope this helps! What sort of applications are you looking at?