  The frustrated pyrochlore iridate Pr$_2$Ir$_2$O$_7$ was proposed as a
metallic quantum spin liquid located at a zero-field quantum critical point.
Here we present the ultralow-temperature thermal conductivity measurements on
the Pr$_2$Ir$_2$O$_7$ single crystals to detect possible exotic excitations. In
zero field, the thermal conductivity shows a dramatic suppression above a
characteristic temperature $T_s \approx$ 0.12 K. With increasing field, $T_s$
increases and the thermal conductivity tends to saturate above $H$ = 5 T. The
Wiedemann-Franz law is verified at high fields and inferred at zero field. It
suggests the normal behavior of electrons at the quantum critical point, and
the absence of mobile fermionic magnetic excitations. The strong suppression of
thermal conductivity is attributed to the scattering of phonons by the spin
system, likely the fluctuating spins. These results shed new light on the
microscopic description on this novel compound.
