The layered compound Ta2NiSe5 is a quasi-one-dimensional and narrow-gap semiconductor, which is proposed to undergo a transition to an excitonic insulator at Tc = 326 K. We found a clear anomaly at Tc in the in-plane thermal conductivities both parallel ( a) and perpendicular ( c) to the onedimensional chains, κa and κc. While κa shows a rapid decrease below Tc, κc shows a pronounced V-shaped suppression centered at Tc. We argue that the decrease of κa represents the suppression of the quasiparticle contribution below Tc due to excitonic condensation. On the other hand, the V-shaped suppression of κc comes from the enhanced phonon scattering by soft phonons associated with the monoclinic transition with momentum q c. The continued suppression of κc up to an extremely high temperature above Tc suggests the persistence of phonon softening likely coupled to electronic, presumably excitonic, fluctuations.