A simple algorithm of velocity scaling is proposed for the isothermal simulation of nonequilibrium relaxation processes accompanied with heat generation or absorption. The algorithm controls the kinetic temperature averaged over an arbitrary time interval at an arbitrary relaxation rate and at an arbitrary velocity scaling interval. The general conditions of controlling temperature are derived analytically and criteria for stable control are established. Our algorithm is applied to simulating the effect of substrate on the "spontaneous alloying" process of metal microclusters [H. Yasuda, H. Mori, M. Komatsu, K. Takeda, and H. Fujita, J. Electron Microsc. 41, 267 (1992)]. The results are compared with the results obtained by the Langevin algorithm in which the kinetic energy of every atom is controlled by respective stochastic heat reservoir. In spite of the marked difference between the two algorithms the relaxation dynamics agree very well in quantity over a sufficient wide range of control parameters. (C) 2003 American Institute of Physics.