I will show that within a non-relativistic quantum-mechanical model of a Universe (the q-Universe) a concept of statistical temperature emerges as a consequence of quantum entanglement between constituents (sub-systems) of the q-Universe. In particular, I will model the q-Universe as a system of interacting spin-1/2 particles described by a specific Hamiltonian (e.g. the Ising model). The q-Universe is assumed to be in a pure state of its Hamiltonian. I will show that (almost) any sub-system of the q-Universe is in a mixed state described by a density operator such that probabilities of outcomes of measurements in the energy eigenbasis of the sub-system are described (can be very well approximated) by the Boltzmann distribution.