A computing system has a thermal manager that changes a power consuming activity limit in the device based on an estimate of temperature of a target location in the system. There are several temperature sensors that are not at the target location. An estimator computes the target location temperature estimate using a thermal model and, as input to the thermal model, data from the sensors. The thermal model produces different estimates of the target location temperature at different ambient temperatures but without computing or measuring the ambient temperatures. Other embodiments are also described and claimed.