Step 1: Examine Statement--I.
Hypochlorous acid is
\[
\mathrm{HOCl}.
\]
On losing a proton,
\[
\mathrm{HOCl \rightarrow H^+ + OCl^-}.
\]
Hence, the conjugate base of hypochlorous acid is
\[
\boxed{\mathrm{OCl^-}}.
\]
Therefore, Statement--I is correct.
Step 2: Examine Statement--II.
The ionic product of water,
\[
K_w=[\mathrm{H^+}][\mathrm{OH^-}],
\]
depends on temperature because the ionization of water is an endothermic process.
Thus,
\[
\boxed{K_w \text{ increases with increase in temperature}.}
\]
Therefore, Statement--II is incorrect.
Hence,
\[
\boxed{\text{Statement I is correct but Statement II is not correct}.}
\]
Therefore,
\[
\boxed{(B)}
\]
is the correct answer.