What Causes Knocking Sounds in a 2012 Impala LT with a 3.6L V6 Engine?

It sounds like you're dealing with a complex issue in your 2012 Impala LT with the 3.6L V6 DI engine. Given that the local Chevy dealer found no diagnostic trouble codes (DTCs) related to the knock sensors, it’s possible that what you’re hearing isn’t actually a knock. Sometimes, the sounds we perceive can be related to the intake air or exhaust pulses, especially at low RPMs when these sounds can be more distinct. As the engine warms up, the sound might change due to the dynamics of the exhaust gases and the temperature of the exhaust piping. You mentioned that the noise is temperature-dependent, which could suggest that it’s related to the exhaust system rather than the engine itself. When the exhaust piping is cold, condensation can affect the sound, and as it heats up, the gas velocity increases, potentially amplifying certain noises. Regarding the carbon deposits you observed in the cylinders, it’s possible that they could lead to pre-ignition, which might produce a knocking sound. This happens when the fuel-air mixture ignites too early due to hot spots created by the carbon. The sound you describe as a "coughing" rather than a "ping" is interesting and could indicate a different issue than typical detonation. Piston slap is another consideration, especially if it’s noticeable when the engine is cold but persists when warm. While some piston slap is normal, continuous noise could indicate a need for service. Other sources of noise could include valvetrain issues, connecting rod noise, or piston pin noise, each with its own characteristics. It’s important to have a thorough inspection to rule out these possibilities. If the noise persists and you’re not able to pinpoint it, consulting with a trusted mechanic who can listen for these specific sounds and conduct a more detailed examination might be your best course of action.