Heat capacity C_P(T) and lattice parameters a(T), b(T) and c(T) of LuB₄₄Si_3.5 borosilicide are experimentally studied as a function of temperature in the range of 2–300 K. The results are compared with those of pseudo-isostructural LuB₅₀ boride. At the lowest temperatures, it is shown that the C_P(T) dependence of borosilicide changes linearly with temperature. This is attributed to the effect of glass-like behaviour of the heat capacity due to the disorder in the sublattice of non-metals. The presence of defects in the B–Si sublattice and the irregular form of the cages in the B–Si matrix, which are occupied by Lu³⁺ ions, lead to the formation of two-level systems (TLS) in the Lu³⁺ subsystem. The TLS make a characteristic bell-like low-temperature contribution to the heat capacity of borosilicide. We show that there is a wide temperature range (5–150 K) of negative thermal expansion of borosilicide, which is attributed to the influence of quasi-independent vibrations of Lu³⁺ ions in the cages of the borosilicide crystal structure.