New advanced and simple two-dimensional (2D) models of sessile droplet heating and cooling and evaporation are suggested. In contrast to the earlier developed one-dimensional (1D) model, based on the assumption that heat supplied from the supporting surface is homogeneously and instantaneously spread throughout the droplet, both new 2D models consider the spatial distribution of this heat. The advanced 2D model is based on the numerical solution to the equations of conservation of mass, momentum, vapor mass fraction, and energy with standard boundary and initial conditions, using COMSOL Multiphysics code. Simple 2D and 1D models assume that droplets retain their truncated spherical shapes during the evaporation process. In the 1D model, the analytical solution to the 1D heat conduction equation inside the droplet is implemented into a numerical code. In the simple 2D model, the 2D version of this equation is solved numerically using COMSOL Multiphysics code. Droplet deformation, temperature gradients along the droplet surface, and the Marangoni effect are not considered in this model. The predictions of all three models are validated using in-house experimental data obtained from studies of sessile droplets of distilled water with initial volumes of 5.2, 3.2, and 2.2 μL, at an ambient temperature of 298.15 K, and at atmospheric pressure. The observed values of normalized droplet radii squared are shown to be close to those predicted by all three models. This allows us to recommend the application of the simplest 1D model for predicting this parameter. The time dependences of the droplet average surface temperature predicted by the advanced 2D model are shown to be close to those observed experimentally. The simple 2D and 1D models can correctly predict the initial rapid decrease in droplet average surface temperature followed by its gradual increase, in agreement with experimental data.