Atomic force microscope (AFM) cantilevers with integrated heaters can topographically map a surface with sub-nanometer vertical resolution, and lateral resolution defined by the shape of the tip. As a resistively heated atomic force microscope (AFM) cantilever scans over a surface, the conductance from the cantilever depends upon the distance between the cantilever to the substrate. By measuring the cantilever electrical resitance signal, which is a function of cantilever temperature, it is possible to topographically map surfaces based. This paper models thermal conductance from the cantilever to make predictions of cantilever sensitivity that compare well with data. The model also predicts noise-limited resolution. Comparing the thermal cantilever with an identically-sized piezoresistive cantilever, the thermal cantilever provides two to four orders of magnitude improvement in sensitivity and up to two orders of magnitude resolution improvement over the piezoresistive cantilever.