Numerical comparisons of temperature measurement through background-oriented schlieren (BOS) and fringe deflection (FD) are presented. Both techniques are based on ray deflection and on the comparison of two different states of a region of observation. A background image displayed on a screen is used in both techniques: for BOS, randomly located spots, and for FD, sinusoidal straight fringes. When a phase object is incorporated into the layout, these spatial structures undergo displacements that are proportional to the gradient of the change of index of refraction. These displacement fields are calculated through digital correlation in BOS and by means of the Fourier phase extraction method in FD. Numerical simulations that model a flame issued by a gas nozzle are presented. The results show that FD presents a slightly larger accuracy for images that either contain relatively high temperature gradients or show low contrast.