A cold start reveals problems that a warm engine hides. Ask your inspection agent to perform and film this sequence.
First, the start itself: the engine should crank smoothly and settle into a stable idle within a few seconds. Extended cranking, blue or white smoke, or a lumpy idle suggest worn internals or head-gasket issues.
Second, listen for timing-chain rattle or metallic tapping in the first ten seconds — cold top-end noise often means deferred maintenance.
Third, watch the exhaust on a cold morning: brief white vapor is normal in winter, but persistent blue smoke means oil burning, and sweet-smelling white smoke can indicate coolant leaking into the cylinders.
Fourth, have the inspector scan the OBD system right after the cold start; misfire counters and fuel-trim values are most honest when the engine is cold.
Ask for a continuous, timestamped video from outside the car before startup through at least five minutes of idling, so you can verify the engine really was cold.