Temperature control of chemical mechanical polishing

A chemical mechanical polishing system, comprising:

• a support to hold a polishing pad;
• a carrier head to hold a substrate against the polishing pad during a polishing process;
• an in-situ monitoring system configured to generate a signal having a value representative of a thickness of a layer on the substrate during the polishing process;
• a temperature control system to control a temperature of a component selected from a surface of the polishing pad, a polishing liquid on the polishing pad, the substrate, or a combination thereof;
• and
• a controller coupled to the in-situ monitoring system and the temperature control system, the controller configured to
• store, prior to polishing, a continuous function that receives only the value representative of the thickness of the layer from the signal and outputs a desired temperature of the component based on the value representative of the thickness, wherein the continuous function is continuous across changes in the thickness of the layer of the substrate, and
• cause the temperature control system to drive the temperature of the component toward the desired temperature output by the continuous function in response to the signal such that the desired temperature and the temperature of the component vary according to the thickness of the layer.