I think you have the gist of it. If you go through the systems in the aircraft flight manuals it gets kind of complicated as to when various valves open or fans operate and doesn't really add much to a practical knowledge of the systems. I have only flown larger Boeings and the A380 where cargo compartment temperatures are selected and monitored from the flight deck, I suspect it is similar for the 737 and A330 although it is possible that there may also be some manufacturer options taken up by different airlines.
PS - I'm also a veterinarian (turned airline pilot), so tend to take an interest in livestock when we carry it.