Or more simply than that, if you only ever look at "cold" and "hot" rooms (e.g. analysis of cancerous and non-cancerous patients) you're never going to see the

Or more simply than that, if you only ever look at "cold" and "hot" rooms (e.g. analysis of cancerous and non-cancerous patients) you're never going to see the dynamics at all. But more fundamentally, I believe there is a theorem which asserts that it is in general impossible to extract the open loop behavior of a system (i.e. a model of how the system would respond without a controller) solely from closed loop data (i.e. data collected from the system when the controller is on.)