This study proposes a simulation-based methodology for estimating the energy saving achievable through the implementation of a just-in-time morning ramp-up procedure in a warehouse (equipped with a heat pump). In this methodology, the operation of the heating supply unit each day is initiated at a different time, aiming at achieving the desired setpoint upon (and not before) the expected arrival of the occupants. It requires the estimation of the ramp-up duration (the time it takes the heating system to bring the indoor temperature to the desired setpoint), which can be provided by machine learning-based models. To justify the corresponding required deployment investment, an accurate estimation of the resulting achievable energy saving is needed. Accordingly, physics-based energy behavior simulations are first performed. Next, various ML algorithms are employed to estimate the ramp-up duration using the simulated time-series data of indoor temperature, setpoints, and weather conditions. It is shown that the proposed pipelines can estimate the ramp-up duration with a mean absolute error of about 3 min in all indoor spaces. To assess the resulting potential energy saving, a re-simulation is conducted using ML-based ramp-up estimations for each day, resulting in an energy savings of approximately 10%.