stubblejumper To be able to decide, I need to understand Read Noise and Image Noise.
To determine how much to cool, you need to check the dark current.
The ASI1600 documentation shows a dark current of 0.03 e/second at 0ºC and .008 e/sec at -15ºC.
A 100 second exposure will therefore produce a dark current of 3e at 0ºC, and the same 100 second exposure will produce a dark current of 0.8e at -15ºC.
The Read noise is mostly independent of temperature, and at the gain of 100 is about 2e. You can't control Read noise (except to change gain and do fewer reads). If the read noise is substantially (say 3 dB to 10 dB) larger than dark currents, then dark current no longer matters.
So, in your case, if you are using 100 second exposures with a gain of 100, you will need to cool the camera to better than 0ºC, but not much more than -15ºC.
It is not that further cooling does not help reduce noise, but because read noise is now the most prominent noise source, and you cannot reduce that by cooling.
Remember that you need to also factor in exposure times. In general, you also only need to get the sky noise to be about 10 dB above camera noise (presumably limited by read noise once you cool the sensor sufficiently). Longer exposures will give diminishing returns (and have other detrimental effects, like Elon Musk's idiotic points of light).
If you have time, check out a YouTube video by Robin Glover (the author of Sharpcap) on parameters to use with modern CMOS cameras.
If you look at an ASI2600, you will see that even at 0ºC, its dark current is already less than 0.002 e/second. The newer models require very little cooling. I never cool my 2600 and 6200 below -10ºC. The lower read noise from the newer cameras also means that I can use shorter exposures.
The saving grace is that the 1600 has a smaller sensor and easier to cool to lower temperatures.
Chen