Upon investigating your attached simulink model I found that the time constant of your mechanical system (heat exchanger) is quite large. Also, there is maximum time delay of 35 seconds. Therefore, you need to increase your simulation time to observe the transients innyour model. I increase the simulation time to 150 seconds in your attached model and was able to get the below attached waveform on the scope.
Now addressing you question about stability:
The system simulated by you is first order system having time delay. Also, it is an open loop system. Therefore, the system will be always stable.
But, if you are planning to add close loop control, then you have to properly design the controller because your open loop transfer function contains large time delays. This will cause the closed loop system to go unstable if the bandwidth of your controller is not properly decided. design a proper controller that ensures good phase margin and gain margin of the overall system.
Also, you will have to compromise on the bandwidth of the over-all closed loop system to account for the large time delays in your loop transfer function.
I hope this addresses your question!
