This paper reports predictions of nanometer-scale polymer deformation during nanoprobe indentation at elevated temperature. The simulations assume continuum polymer properties with modified boundary conditions to model subcontinuum polymer mechanical deformation. The indenter is a heated atomic force microscope (AFM) tip, and the media is a high molecular weight polymer film where tip radius, film thickness, and polymer coil radius are of similar size, in the range 20-50 rim. The simulations model isothermal conditions, where the tip and polymer are at the same temperature, or nonisothermal conditions, where the tip is hot while the polymer is cool. Isothermal simulations with shear-thinning bulk material behavior and full-slip polymer-tip interface predict force, displacement, and displacement rate. Nonisothermal simulations show that the polymer-tip interface temperature governs the indentation process. The temperature-dependent polymer viscosity varies by several orders of magnitude within 50 nm of the polymer-tip interface, causing highly localized polymer deformation near the tip. Steep viscosity gradients near the tip require the polymer-tip interface temperature to exceed the polymer glass transition temperature in order to form indents. In all cases the predictions compare well with experimental data. The continuum simulations allow for improved understanding of high-temperature AFM nanoindentation and nanoembossing.