On the basis of computer-simulation results for three different models with soft domain walls it is argued that the zero-temperature domain-growth kinetics falls in a separate universality class characterized by a kinetic growth exponent n0.25. However, for finite temperatures there is a distinct crossover to Lifshitz-Allen-Cahn kinetics n=0.50, thus suggesting that the soft-wall and hard-wall universality classes become identical at finite temperatures.