How to control model discrete system with time delay #697

I would like to control temperature calibration bath. The regulator is two state switch (heater on, heater off).
System has delay about 80 sec., my sampling period is 2 sec , system can be simulated as IIR low-pass filter.
I recorded heater state and bath temperature for heating and cooling phase, so I have input signal and system response.

I would like to control system to stabilize temperature as quick as possible.
I tried to calculate IIR filter coefficients in excel with solver, it fits well for heating and cooling but results are unstable when I try predict temperatures (results goes to infinity after about 100 iterations - 200 sec.)

I will be grateful for any suggestions how to control this device or how to find z transmitance of device.