In this work, the variational Monte Carlo (VMC) method using the restricted Boltzmann machine (RBM), a feed-forward neural network, is investigated to allow for the computation of finite-temperature results of quantum spin models in one and two dimensions. To accomplish this task, there are, at least, three different approaches possible that are discussed and compared for the Heisenberg model in one dimension before they are deployed to the Heisenberg and the $J_1$-$J_2$ model in two dimensions. In the latter case, the correct detection of the presumed finite-temperature phase transition is studied. The three different types of methods studied in a variational setting are comprised by the purification method, the sampling method, and the use of variational thermal pure quantum states and thus the notion of quantum typicality. In the proceeding of this study, the reason for choosing the RBM as the predestined variational ansatz is motivated by general (artificial) neural network theory and investigations and findings related to the ground state optimization method. In the purification and the sampling method, finite temperature correlation functions for the one-dimensional Heisenberg model are computed successfully and even the free energy is attainable. Unfortunately, the idea of using quantum typicality in a combined variational ansatz, using the RBM and a pair-product ansatz, is shown to lead to inaccurate results at low temperatures due to the high entanglement entropy of those variational states. The issue seems to be persistent for any variational ansatz wave function and renders the applicability of quantum typicality in a variational setting highly problematic. To complete this investigation, the real-time evolution at infinite temperature is studied and the unfavourable scaling of the number of hidden units documented. Finally, the purification and the sampling method are applied to the $J_1$-$J_2$ model on the square lattice. Unfortunately, the computation of accurate results for very low temperatures is difficult due to an increase in the rejection probability, an issue related to the Monte Carlo sampling and known as critical slowing down.