The temperature dependences of the elastic constants and thermal expansion of a Cr-Al-alloy single crystal containing 2.2 at.% Al are reported. This is a critical concentration, being simultaneously close to the very steep incommensurate-commensurate spin-density wave transition line on the magnetic phase diagram as well as to the triple point, where the incommensurate and commensurate spin-density wave states coexist with the paramagnetic state. Very large magnetic contributions at 0 K of up to 28% for cL= 1/2 (c11+c12+2c44), 24% for c11 and 48% for the adiabatic bulk modulus, B, were observed, while the magnetic contributions to the shear elastic constants, c44 and 1/2 (c11-c12), amount to less than 1% at 0 K. The magnetovolume, the longitudinal elastic constants as well as B vary linearly with temperature over a large temperature range, This cannot be explained by existing theories. The absolute value of the zero-temperature magnetic Gruneisen parameter is exceptionally large, reflecting the much larger magnetic contribution to B than to the volume of the crystal at 0 K.