The objective of this work is to quantify the relationship between thermal efficiency and dynamic controllability. For a given feed-effluent heat exchanger (FEHE), relationships between the degree of heat recovery and open-loop poles are derived. Then, similar to the ultimate gain in the control literature, the ultimate heat recovery can be derived. By ultimate heat recovery, we mean the amount of heat recovery such that the open-loop system is at the limit of stability (i.e. having poles at the imaginary axis). Since the controllability is characterized by the pole locations, achievable closed-loop performance of heat integrated systems can also be evaluated, internal as well as external energy load disturbances are compared. The results clearly quantify the trade-off between the thermal efficiency and controllability. More importantly, the results presented here offer a simple way to synthesize a controllable heat integrated reactor.