When you set up the Thermostat correctly, it will control the amount of current that is flowing to the heatmat, thus keeping the heatmat at a constant temperature.
however, you will find that there are different types of thermostats out there. You have the kind that turn something on and off, and you have the regulator type that just regulate the current.
For all of you that aren't electrically savvy, current is the flow of electrons from a negative terminal to a positive terminal. Voltage, when applied to a resistance source, is what creates the current. When you change the resistance that the voltage is going through, you will increase or decrease the amount of current going to the powered object in question. example: The type of thermostat that regulates current is made up of a rehostat (variable resistor (dimmer switch)) that is controlled by a microcomputer. The Microcomputer then has a measuring protocal that will take the temp of a certain area (where the probe is) and compare it against the user settings (constant). If the measured < constant then the thermostat lowers the amount of resistance, thus increasing the amount of current. If measured > constant, the thermostat increases the amount of resistance to lower the current. If measurement = constant then everything is gravy and the thermostat doesn't make any changes.
The above statement is proved by using Ohm's Law (V=IR --> where V=Voltage, I=Current, and R=Resistance). When you are looking for the amount of current, you change the equation to be I=V/R. Thus, I and R are inversely proportional. So, if you increase R, you decrease I, and if you Decrease R, you increase I.
Hope this helps all to know more how a thermostat works. If this is a little too technical, let me know and I will convert it to none techie talk.