Step 1: Define an isobaric process.
Isobaric literally means equal pressure, so the defining feature is that the pressure of the system stays constant ($\Delta P = 0$) while other quantities may change.
Step 2: Check statement (A).
It says the pressure remains constant. This is exactly the definition, so it is correct.
Step 3: Check statement (B).
Work done at constant pressure is $W = P\,\Delta V$. For work to occur the volume must change, so a volume change accompanying work is correct.
Step 4: Test statement (C) using the gas law.
At constant pressure, $PV = nRT$ reduces to $V \propto T$ (Charles' law). So when the volume changes, the temperature must change too - it cannot stay constant. A constant-temperature process is isothermal, not isobaric. Hence statement (C) is the wrong one.
Step 5: Check statement (D).
The first law $Q = \Delta U + W$ shows that the heat supplied at constant pressure both does expansion work and changes the internal energy, so this statement is correct.
Step 6: Identify the incorrect statement.
Only statement (C) contradicts the physics of an isobaric process.
\[ \boxed{\text{Wrong statement: (C) temperature remains constant}} \]