It was recently discovered that, depending on their symmetries, collinear antiferromagnets may break spin degeneracy in momentum space, even in the absence of spin-orbit coupling. Such systems, dubbed altermagnets, have electronic bands with a spin-momentum texture set mainly by the combined crystal-magnetic symmetry. This discovery motivates the question of which novel physical properties derive from altermagnetic order. Here we show that one consequence of altermagnetic order is a fluctuation-driven piezomagnetic response. Using two Heisenberg models of d-wave altermagnets, a checkerboard one and one for rutiles, we determine the fluctuation-induced piezomagnetic coefficients considering temperature-induced transversal spin fluctuations. We establish in addition that magnetic fluctuations induce an anisotropic thermal spin conductivity.