Step 1: Check each option
$\Delta V=0$, $W=0$ and $Q=\Delta U$ are all true for an isochoric process.
Step 2: Remaining option
$\Delta T=0$ is the condition for an isothermal process, not isochoric, so it is the untrue statement.
Step 3: Final answer
The statement $\Delta T=0$ is the one that is not true for an isochoric process.
Final Answer:
Only Delta T equals zero is false for an isochoric process.
\[ \boxed{\text{(A) }\Delta T=0} \]