Numerous micro-cutting simulations have been proposed by using molecular dynamics (MD), in which the temperatures of an outer boundary are kept constant by assuming a steady state. Present paper investigates the treatment of temperature distributions of the boundary in the vicinity of the tool edge comparing between steady and unsteady, in the case of cutting force per unit width, morphology of chip deformation and temperature distributions. As a result, giving unsteady temperature distribution to the boundary is more desirable to the analysis than steady one. In the case, temperature distributions in the vicinity of the tool edge under unsteady boundary condition agreed well to the results under broad boundary condition.