The sudden change of moisture and/or temperature on a solid can significantly disturb the resulting stresses and strains and cause material damage. This investigation is concerned with the sudden rise (or drop) of temperature over a finite segment of a half-space that is free of tractions. The mutual dependence of moisture and temperature is examined by coupled equations such that the hygrothermal stresses and strains are transient in character. The moisture, temperature, and stress are computed by a time-dependent finite-element method and are found to peak and oscillate as a function of time in the vicinity where the surface temperature is altered. These effects are displayed for the 5208 epoxy resin material commonly used in fiber-reinforced composities.