Hysteretic nonlinear elasticity is often observed in consolidated granular media, including concrete, mortar, sandstones, or rocks. Nonlinearity is frequently quantified using Nonlinear Resonant Ultrasonic Spectroscopy (NRUS), which provides tools to define nonlinear parameters for both fast and slow dynamic effects, often observed when analyzing the propagation velocity dependence on strain in such materials. The dependence of these parameters on temperature was studied with the aim of using NRUS to quantify the induced thermal damage; thus, experiments were performed spanning a wide temperature range. However, since most of these materials are used in construction (concrete and sandstone, mostly), it is of interest to understand how sensitive the measured nonlinear parameters are to small environmental temperature fluctuations. In this paper, the dependence on temperature of elastic parameters is investigated, both linear (wave velocity and damping) and nonlinear (the slope and hysteresis of the curves describing the strain dependence of wave velocity and residual conditioning effect on wave velocity), separating the slow from the fast dynamic properties of nonlinearity. The observations reported here denote a different behavior for concrete and Berea sandstone.@en