Neural architecture search (NAS) targets at finding the optimal architecture of a neural network for a problem or a family of problems. Evaluations of neural architectures are very time-consuming. One of the possible ways to mitigate this issue is to use low-fidelity evaluations, namely training on a part of a dataset, fewer epochs, with fewer channels, etc. In this paper, we propose a bayesian multi-fidelity method for neural architecture search: MF-KD. The method relies on a new approach to low-fidelity evaluations of neural architectures by training for a few epochs using a knowledge distillation. Knowledge distillation adds to a loss function a term forcing a network to mimic some teacher network. We carry out experiments on CIFAR-10, CIFAR-100, and ImageNet-16-120. We show that training for a few epochs with such a modified loss function leads to a better selection of neural architectures than training for a few epochs with a logistic loss. The proposed method outperforms several state-of-the-art baselines.