The temperature and velocity field, pressure distribution, and the temperature variation across the sample region inside an environmental transmission electron microscope (ETEM) have been modeled by means of computational fluid dynamics (CFD). Heating the sample area by a furnace type TEM holder gives rise to temperature gradients over the sample area. Three major mechanisms have been identified with respect to heat transfer in the sample area: radiation from the grid, conduction in the grid, and conduction in the gas. A parameter sensitivity analysis showed that the sample temperature was affected by the conductivity of the gas, the emissivity of the sample grid, and the conductivity of the grid. Ideally the grid should be polished and made from a material with good conductivity, e.g. copper. With hydrogen gas, which has the highest conductivity of the gases studied, the temperature difference over the TEM grid is less than 5 C, at what must be considered typical conditions, and it is concluded that the conditions on the sample grid in the ETEM can be considered as isothermal during general use.