Quiet PC cases are specially designed to reduce noise using features such as noise-damping foam to absorb the vibrations from the spinning hardware. In some cases, very quiet cases can result in poor airflow causing your PC to heat up.
Ultimately, the airflow of your PC case comes down to the design. Our top pick, the Fractal Design Define 7 claims to have excellent airflow and cooling capabilities. In this case, this should not be a concern.
When choosing your next PC case, we recommend reading over the specifications and checking reviews to make sure buyers have not encountered issues with overheating. We also recommend considering how much noise you would be happy to withstand so you are not compromising on thermal performance.