The effect that filler size and content exerts on the out-of-plane effective thermal conductivities (TCs) of hexagonal boron nitride (hBN) and Kapton-type polyimide (PI) (hBN/PI) composite sheets was investigated in an effort to enhance the TCs of Kapton-type PI sheets. A TC-measurement apparatus that was devised based on the steady-state method was adopted. The apparatus was constructed in-house, and its validity was established. In this study, the effective TCs of composite sheets were increased with increases in the hBN size and volume fraction. The enhancement behaviors of the effective TCs obtained in the present work reasonably approximated the data in the literature regardless of the differences in either the preparation method of the composite or the monomer species of the PI. The Hamilton and Crosser model could reproduce the experimentally enhanced levels of effective TCs for all hBN/PI composites via adjustments to the configuration factors for hBN.