  Resistivity and specific heat have been measured on a single crystalline
sample of the beta-pyrochlore oxide superconductor, KOs2O6. It is found that a
second peak in specific heat, which may evidence an unknown phase transition,
appears around Tp ~ 7.5 K below the superconducting transition temperature Tc =
9.53 K. Applying magnetic fields up to 14 T, Tc is reduced gradually down to
7.1 K, while Tp is raised a little and becomes even higher than Tc at 14 T,
which implies that the second anomaly is not associated directly with the
superconductivity. It is demonstrated, however, that there is significant
communication between the two anomalies, suggesting that they come from the
same electrons. It is also reported that the Sommerfeld coefficient ? in KOs2O6
is possibly much larger than in other members of beta-pyrochlore oxide
superconductors, RbOs2O6 (Tc = 6.3 K) and CsOs2O6 (Tc = 3.3 K).
