When the resistance of the thermistor changes due to changes in temperature, the fraction of the supply voltage across the thermistor will also change producing an output voltage which is proportional to the fraction of the total series resistance between the output terminals.

What happens to voltage when thermistor temperature increases?

Most things just called a "thermistor" exhibit decreased resistance with rising temperature. There are also such things as PTC (positive temperature coefficient) thermistors that exhibit the opposite effect. As you say, V = IR. If R goes down, the V will go down at the same I.

Does a thermistor produce voltage?

Figure 4: Thermistor Controlled System

The controller can't read resistance, so it must convert resistance changes to voltage changes by using a current source to apply a bias current across the thermistor to produce a control voltage.