Synthetic jet (SJ) impingement cooling is a promising technique for enhancing convective heat transfer in compact thermal management systems. While the behaviour of single jets is well understood, practical applications require multiple jets operating in close proximity. In such configurations, strong nonlinear interactions between neighbouring jets significantly alter the flow structure and cooling performance, making accurate prediction challenging. This study develops an integrated computational, experimental, and machine-learning framework to predict the thermal behaviour of multi-SJ arrays. Transient CFD simulations, validated using hot-wire anemometry, are employed to characterise jet dynamics and generate a dataset spanning key non-dimensional parameters, including Reynolds number (Re), the jet-to-surface spacing (H/D), lateral spacing (S/D), stroke length ratio (L/D), and actuation frequency. Conventional data-driven models trained on single-jet data fail to generalise to multi-jet configurations, while models trained on combined datasets remain restricted to fixed geometries. To overcome this limitation, a Modular Jet-wise Reconstruction framework is proposed, in which local single-jet predictions are superposed and augmented with an interaction-aware correction model to capture nonlinear jet-jet effects. The proposed framework enables accurate prediction across the investigated range of varying inline jet configurations without retraining, while achieving a computational speed-up of approximately 107 compared to transient CFD. This provides a computationally efficient framework for multi-jet cooling within the investigated configuration and parameter ranges and enables rapid design exploration.