System Id on system with tank

I'm trying to model a system with a tank with a fluid that runs through a cooler and heater to run temperature control on it. A temperature sensor in the tank monitors the temperature. I have been able to run the system open loop to collect data for a system identification, I'll pulse the heater and the cooler independently and then fit the data with the system id toolbox. One of the problems is the tank functions like a giant integrator and the system id has trouble with the lower frequency dynamics. Is there any way to get the short term dynamics of the cooler or heater separate from the longer frequency tank dynamics from data that has both?