As we stack images the level of noise does of course add up but the profile across the top of it becomes smoother. The stacking software deals with the increasing level by adding into deeper images than those originally coming from the camera (32 bits per colour channel rather than 16, allowing a much greater range of brightness values).
Thermal noise, as its name suggests, is worse at higher temperatures. So doing astrophotography on a freezing cold night may not be so good for us but it does make for less noisy images.
It is also worth pointing out that the LCD display on the back of many cameras generates heat if it is switched on, and it lies right behind the detector. So do not use a live view on the camera while photographing. Leaving some time between exposures also gives the detector a chance to cool down.
Noise reduction in camera is not designed for our application. It is more likely to be used for shooting in a darkened room. Its aim is to smooth the darker parts of the image. In doing so it may lose the faint detail that we are after, which is only just a little brighter than the background.
Also do not use the extended ISO settings that may be available in the menu system of your camera (in my Canon camera they are called H1 and H2). It is believed that they amplify the image by software after digitisation and therefore reduce the dynamic range available in the image. ("Believed" because camera makers do not publish such information.)