In a previous study of isomerization dynamics of clusters as a chaotic conservative system, we proposed a temperature, called the microcanonical temperature [C. Seko and K. Takatsuka, J. Chem. Phys. 104, 8613 (1996)], which is expected to characterize a phase space distribution on a constant energy plane. In contrast to the standard view of equal a priori distribution in phase space, we note a fact that this distribution usually becomes sharply localized with a single peak, if projected onto the potential energy coordinate. The microcanonical temperature is defined as a kinetic energy at which this projected distribution takes the maximum value. Then the most probable statistical events should be dominated by those components in vicinity of the peak, provided that the projected distribution is singly and sharply peaked and the associated dynamics is ergodic. The microcanonical temperature can be similarly redefined in the individual potential basins. Here in the present article a numerical fact is highlighted that the inverse of the lifetime of an isomer bears an Arrhenius-type relation with thus defined local microcanonical temperature assigned to the corresponding potential basin. We present an analysis of how the Arrhenius relation can arise.