Because your idle speed has been adjusted to compensate for the fact that you are always running with the same amount of additional air. After you replace the t-stat you will have to adjust the idle air screw as it won't run when the car warms up as you have surmised. Remember engine speed is determined by air not fuel! To raise engine speed air must be added.
BTW the t-stat does not open or close it just gets longer as it warms and shorter when it cools. This action moves the piston below the t-stat which is the air slide. REMEMBER it may not be the t-stats fault. If the air slide piston is frozen open a new one will not fix it. I would verify the movement before replacing. I would replace though as I think the t-stat will not be very good after trying to push a frozen piston for a while. It is very likely that it will be frozen as no movement usually leads to such. (or is such).
The piston is in the housing below the t-stat cylinder. They are easily cleaned/freed up. Drain your coolant and pull the t-stat housing (cylinder) - two screws. With the t-stat removed push on the piston where the t-stat plunger sat. It should be spring loaded up. It should easily push down and spring back. If not remove the other two screws and take the housing to the bench to free up. NOTE: there are shims beneath the t-stat and beneath the housing. Besure to replace them as they were.
Bosch Master, ASE Master, L1
33 years MB technician