A control system for an engine having a catalytic converter includes an energy calculation module that calculates a calculated mass air flow (MAF) of intake air of the engine based on a requested torque and a requested spark timing that correspond to a desired thermal energy of exhaust of the engine, and that determines an expected thermal energy of the exhaust based on the calculated MAF, and an energy residual module that determines a thermal energy residual of the exhaust based on the expected thermal energy and an estimated thermal energy of the exhaust, wherein the estimated thermal energy is based on a measured MAF of the intake air. The control system includes an energy evaluation module that determines a diagnostic result that indicates whether the catalytic converter is operating within a target temperature range based on the thermal energy residual. Related control methods are also provided.