Temperature dependences of elastic constants, $с_{ij}(T)$, of Zr-based bulk metallic glasses (BMG), Zr$_{41.2}$Ti$_{13.8}$Cu$_{12.5}$Ni$_{10}$Be$_{22.5}$ and Zr$_{52.5}$Ti$_{5}$Cu$_{17.9}$Ni$_{14.6}$Al$_{10}$ (at.%), are studied in detail within the range of temperature from 78 K up to 300 K using resonant ultrasound spectroscopy. The results enable one to determine the temperature behaviour of both the mechanical properties–the shear, longitudinal, bulk elastic moduli, the Poisson’s ratio, and the vibrational characteristics–Grüneisen parameters and Debye temperature. Analysis of $с_{ij}(T)$ is based on the physical model of the close packing of atomic clusters with icosahedral symmetry of atomic ordering.