The bounds of the heat production rate within the moonA new approach is proposed to the evaluation of the lower and upper bounds of the global heat production rate within planetary interiors. The approach is based on the relationship between the internal energy change and the volume change of a planetary object. For illustration, the approach is applied to the moon. Using an average global surface heat flux of 18 erg/sq cm-sec, and assuming constancy of the lunar radius during the past 3.2 billion years. the lunar heat release within the past 3.2 billion years is estimated at (30 to 40) x 10 to the tenth erg/cu cm. This is equivalent to the present day uranium concentration of 35 to 50 ppb provided the radiogenic isotopes are of the same proportion as that given by Toksoz et al. (1978).