The problem of phase stability is one of the key problems in the study of high-entropy alloys. Here we address this issue for a heat-resistant high-entropy TiZrHfNb alloy with a bcc structure. The evolution of the structure of this alloy is studied during isothermal annealing at T = 400 °C. It was found that the as-cast alloy consists of two coexisting bcc phases with similar unit cell parameters. This state is homogenized during annealing. Still, the highly stressed nanostructured state is retained and the texture is enhanced. The thermal conductivity of the alloy in the temperature range of 20-400 °C changes in the range of 8-16 W m K, which is comparable in order of magnitude with the thermal conductivity of steels.