We present a real time, in situ method to control the spatial temperature uniformity of a semiconductor substrate during the various bake steps in the lithography sequence. Significantly, the wafer temperature settles down to steady state within 50 s under closed-loop control. The corresponding maximum temperature nonuniformity during transient is less than 1 degrees C and the steady state temperature nonuniformity is less than 0.1 degrees C. Specifically, we have developed a complete thermal diffusion model for the entire bake plate-and-wafer system, so that the transient thermal behavior is accurately captured during the baking process. By monitoring the bake plate temperature and fitting the data into the model, an updated model can be estimated and the desired wafer temperature can then be calculated and controlled in real time. Experimental results confirm the efficacy of the approach and its superiority over traditional run-to-run control techniques.