The Kinetic Theory of Gases explicitly states that the average translational kinetic energy of a molecule is solely a function of temperature: $\bar{K}=\frac{3}{2}{k}_{B}T$.

• If the temperature is constant, $\bar{K}$ remains the same.
• A pressure increase at constant $T$ must be caused by an increase in number density ($N/V$, i.e., compression), not by the individual molecules hitting the walls harder on average.