## 1 Introduction  
Consolidated granular media, which are frequently utilized in construction and building technology (e.g., rocks and sandstones [1, 2, 3, 4], concrete [5, 6], mortar [7], etc.), exhibit a strong nonlinear elastic behavior, which is often significantly enhanced when damage is present. Such behavior is characterized by the presence of hysteresis in the dependence of the wave velocity and damping on strain, which might be seen as originated by slow dynamics [8, 9, 10, 11, 12]. The latter is indeed the main evidence of hysteresis and memory effects. This phenomenon is due to the existence of the equilibrium states of the material, characterized by given viscoelastic properties (modulus [13] and damping [14]), which are dependent on the strain applied (drive strain amplitude). The relaxation to such an equilibrium state is a long-term relaxation process, which could be described as a multirelaxation phenomenon [15, 16, 17].  
Nonlinear elastic hysteresis is often evident even at low strain levels (of the order of \(10^{-7}\)), with variations in the propagation velocity of the order of percent (and much higher damping variations). Several techniques have been developed to detect such a small nonlinearity, mostly applicable to small samples: Nonlinear Resonant Ultrasound Spectroscopy--NRUS [18; 19; 20]; the Scaling Subtraction Method--SSM [21; 22], Nonlinear Elastic Wave Spectroscopy [23; 24], etc. All these methods show that the nonlinear effects are significantly stronger when materials are damaged, thus providing an efficient tool for nondestructive testing.  
Studies reported in the literature show the strong sensitivity of nonlinear parameters to damage evolution: quasi-static loading-induced damage [25; 26], thermal damage [27; 28; 29], chemical damage [30; 31; 32], etc. However, to make nonlinear ultrasonic methods a tool to quantify damage, it is necessary to separate the nonlinearity increase due to microstructural changes from those due to environmental effects (in the environmental range). While some studies have been reported to study humidity's effects on the hysteretic elasticity [18; 33; 34; 35], fewer studies are devoted to analyze temperature effects.  
Most of them include thermal damage to the material [27; 28; 29] or aim to analyze how temperature changes might induce slow dynamic effects [36; 37]. Some studies have reported the effects of temperature inducing low levels of damage [29] or have monitored the evolution of nonlinear rock parameters while the temperature varies, i.e., not at equilibrium [38]. On the contrary, results are available showing the dependence of linear elastic parameters on temperature [39; 40].  
Here, the work focuses on analyzing the dependence of linear and nonlinear elastic parameters in the environmental temperature range, avoiding transient regimes. Concrete and sandstone samples have been studied, with the aim of quantifying the influence of temperature on the measured nonlinearity and, in particular, its order of magnitude compared to the order of magnitude of damage-induced nonlinearity variations. In Section 2, details about the experiment and material tested are given, together with a recap on the NRUS method. The results are reported in Section 3. The temperature dependence of the linear and nonlinear elastic parameters is discussed in Section 4, while the discussion and conclusions are reported in Section 5.