Fully resolved simulations are used to quantify the effects of heat transfer in the absence of buoyancy on the drag of a spatially fixed heated spherical particle at low Reynolds numbers ($Re$) in the range $10^{-3}\leqslant Re\leqslant 10$ in a variable-property fluid. The case where buoyancy is present is analysed in a subsequent paper. This analysis is carried out without making any assumptions on the amount of heat addition from the sphere and thus encompasses both the heating regime where the Boussinesq approximation holds and the regime where it breaks down. The particle is assumed to have a low Biot number, which means that the particle is uniformly at the same temperature and has no internal temperature gradients. Large deviations in the value of the drag coefficient as the temperature of the sphere increases are observed. When $Re<O(10^{-2})$, these deviations are explained using a low-Mach-number perturbation analysis as irrotational corrections to a Stokes–Oseen base flow. Correlations for the drag and Nusselt number of a heated sphere are proposed for the range of Reynolds numbers $10^{-3}\leqslant Re\leqslant 10$ which fit the computationally obtained values with less than 1 % and 3 % errors, respectively. These correlations can be used in simulations of gas–solid flows where the accuracy of the drag law affects the prediction of the overall flow behaviour. Finally, an analogy to incompressible flow over a modified sphere is demonstrated.