  We present here the temperature dependence of heat capacity ($C$($T$)) and
thermal conductivity ($\kappa$($T$)) in the superconducting state as well as in
the normal state of as-cast V$_{1-x}$Zr$_x$ alloys. Distinct jumps in the
$C$($T$) of the alloys indicate the presence of three superconducting phases
with transition temperatures $T_{C1}$ = 5.4~K, $T_{C2}$ = 8.2~K and $T_{C3}$ =
8.5~K. From the metallography micrographs, these three phases are identified to
be $\beta$-V, $\gamma$-ZrV$_2$, and $\gamma'$-ZrV$_2$ respectively. Apart from
these phases, $\alpha$-Zr and $\beta$-Zr phases are also detected in these
samples. The experimental $\kappa$($T$) in the superconducting state of these
alloys is observed to be significantly higher than that expected theoretically.
Our analysis suggests that the above observation is due to the coexistence of
multiple superconducting and non superconducting phases which resulted in the
two-parallel channels for the conduction of heat.
