We have performed numerical calculations to study the generation of arbitrary temperature profiles with high spatial resolution on the surface of a solid. The characteristics of steady-state distributions and time-dependent heating and cooling cycles are examined, as well as their dependence on material properties and device geometry. Ideally, low-power consumption and fast response times are desirable. The simulations show that the achievable spatial resolution is on the order of the substrate thickness and that the response time t1 depends on the width of the individual heating elements. Moreover, the rise time t1 can be significantly shortened by deposition of a thermal insulation layer, which also reduces the power consumption and increases lateral resolution.