[throwaway9870]

I think you are confusing terms. You are saying latency, but I think you mean the time constant of the poles / zeros. When one speaks of latency in a control system, they general mean a real time delay, like a digital processing delay, communication delay, etc. When you speak of something having low-bandwidth, such as due to the thermal mass and heating element you are describing, then one would say it has a long time constant. I have never seen these systems any harder to implement with a PID provided you select the proper terms to keep it stable. If it is just a linear PID, it is going to need to be a slow loop in this case.