Cooling of astrophotography camera sensor chip
The practical length of the time exposure will depend on your equipment. Cameras used in astrophotography are generally able to be used with exposure times ranging from milliseconds to hours. As your question stands, cooling the chip will have no effect on the length of the exposure time. What it can affect is the amount of noise in the image. Cooling the sensor generally reduces the amount of noise. Cooling beyond -20°C may have limited value, particularly if you are not using research-grade instruments. While you may further reduce the noise, you may still be at the mercy of the quality of the optics, drive mechanisms, etc. and you may have less noise in the image but the limiting factor is not your image noise but the system limit for drift and distortion.

Some professional instruments use liquid nitrogen cooling while others use thermoelectric cooling, depending on the manufacturer and the intended use. The instruments that use sub-zero cooling also usually have a high quality sensor with a pixel well depth that supports longer exposures, without bleeding effects from adjacent pixels. It all depends on the sensor, camera, and other parts of the system, so your mileage may vary.