Well, the temperature control and the remote monitored variables probably aren't air-gapped. So if you gain access to the remote monitoring, you're already in the system, from where you can attack the rest of the system. Ofcourse you could design the system so that there's no link between the monitored stuff and the rest, but then you'd need extra components so there's a financial driver not to do this if you build this kind of equipment.
Edit: this is all assuming that the system isn't by design remote controllable, and my guess would be that it probably is. It allows equipment builders/suppliers to help their customers with "remote troubleshooting".