Cascade Control System - Multi-Stage Temperature Control
In a former life, I designed and built automated test stands for engineered fluid handling components and systems. PID control is the way to go, I always started with a manual method and tweaked later and of course we did plenty of system testing to validate before turning the thing loose. 

I'd stick with one active PID loop at a time, though depending in the state of your system, you might switch between them. Say one for warmup and another for operation. 

I think you're going to have a hard time with the system as it's set up now, I have some questions you might consider. 


Is there a reason the fluid circuit is open loop? 
could you recirculate? 
could you have a bypass loop and when ready to run, simply switch a valve?