Acoustic velocity dispersions in three rocks saturated with water, normal decane (n‐decane), and a heavy oil (in petroleum engineering, heavy oil is referred to as crude oil with viscosity higher than 0.5 Pa s), respectively, are calculated in this paper. The results show that the apparent velocity dispersion in light fluid (low‐viscosity)‐saturated rocks is relatively small, usually less than 3% to 5%, whereas that in the same rocks saturated with heavy oil is much larger. Such apparent velocity dispersion can be well explained by the ‘‘local flow’’ mechanism, which relates dispersion to the viscosity of the pore fluid, the pore geometry of the rock, and the effective pressure and temperature. The Biot velocity dispersion calculated using the Gassmann equation and the Biot high‐frequency limit of the velocities in the rocks is very small, typically less than 2%. Such Biot dispersion can be explained in terms of the Biot theory, which relates dispersion to the viscosity of the pore fluid and the permeability of the rock in a way that is just opposite to the local flow mechanism. According to either the local flow mechanism or the Biot theory, the temperature dependence of the compressional wave velocities inheavy‐oil‐saturated rocks in the seismic frequency band should be no less than that observed in the laboratory at 0.8‐MHz frequency, which means that the laboratory results can be applied to the field as a basis for seismic monitoring of thermal floods.