The distributed thermal processes are widely present in various industrial operations, but the presence of time delay effect and unknown model information make achieving fast and timely fault detection challenging. Furthermore, the involvement of spatiotemporal coupled data in measurement processes further exacerbates the situation. To solve these problems, this paper proposes a data-driven fault detection and location method for thermal processes described by distributed parameter systems (DPS). Firstly, a Time/Space separation is employed to decoupling the spatio-temporal data into spatial basis functions and temporal coefficients. Subsequently, dynamic partial least squares (DPLS) is employed to obtain the temporal information of the model with fault-free data. Monitoring statistics in both the temporal and spatial domains are then constructed, and their thresholds are estimated by kernel density function. Finally, an online strategy for fault detection and location is presented. The method was validated on the catalytic rod, and an experimental snap curing oven.