For complex thermal processes under multi heat source coupling, the various heat sources in the system not only have complex thermal dynamics but also differ from each other. The thermal behavior of each heat source also affects the temperature distribution of other nearby heat sources, which makes it challenging to achieve accurate control of the DPS. Aiming for this problem, a spatiotemporal fuzzy control approach is proposed for unknown and complex DPSs. First, a multi heat source coupled spatiotemporal fuzzy control strategy based on double-layer fuzzy rules and parallel compensation control approach was designed. To ensure the stability of the controller, the stability conditions of the system were theoretically derived, and the controller achieved stable control of multi heat source coupled thermal processes in different spatial regions. Stability conditions of the control system are rigorously deduced by transforming the solving process to a series of linear matrix inequalities (LMIs). The stability and effect of the proposed spatiotemporal control strategy are demonstrated by mathematical proof and case studies.