The boundary element method (BEM) has been producing positive results in fields where analysis is possible only by boundary integration, such as elastostatics problems. However, in natural vibration analysis using the fundamental solutions of elastostatics, or internal heat generation or initial temperature distribution in unsteady heat conduction analysis, domain integration is required. Authors have developed an efficient equivalent mass method for nutural vibration analysis problems and has been applying it to actual equipments. In this paper authors try to apply the equivalent mass method to problems involving domain integrals of unsteady heat conduction analysis.