Axion-like particles, including the QCD axion, are well-motivated dark matter candidates. Numerical simulations have revealed coherent soliton configurations, also known as boson stars, in the centers of axion halos. We study the evolution of axion solitons immersed into a gas of axion waves with Maxwellian velocity distribution. Combining the analytical approach with controlled numerical simulations, we find that heavy solitons grow by condensation of axions from the gas, while light solitons evaporate.