We present a sensitive heat capacity measurement method for use at temperatures between 300 and 700 K using a home-made calorimeter incorporating a Si-N membrane microcalorimeter and a commercial tube furnace. We employ a scanning relaxation method with the two relaxation times, in which temperature is scanned with a maximum speed up to similar to 30 K/min to measure the heat capacity of sub-mg single crystals. The heat capacity of the addenda composed of the Si-N membrane and thermal grease is measured to be as small as similar to 30 mu J/K. For the high temperature thermal grease, several materials such as In, Wood's metal, and silicone oil have been tested. We demonstrate the Successful performance of this method with different scanning speeds by measuring the specific heat of Cu up to 620 K. A brief summary of advantages/disadvantages of this method vis-A-vis commercially available differential scanning calorimeters (DSCs) is given. (C) 2008 Elsevier B.V. All rights reserved.