Macroscopic temperature is a measure of the average kinetic energy of a group of molecules. Those molecules which are colliding with the face of the piston have their velocity increased due to their elastic collision with a moving boundary - the piston face. Therefore, as a group their rebound velocity and their temperature is increased. As a group, these molecules do have a higher temperature than those at the other end of the cylinder and there is a temperature gradient in the cylinder. This gradient is reduced by heat that is transferred through the working gas.
If you speed up your observations, you will realize that the increase in molecular or atomic velocity immediately after rebound from the piston face is not random. The increase is entirely along the axis of piston face movement. As this is not purely random motion, one can ask if it is really thermal energy at all or if it is not more correctly viewed as flow energy and you can reasonably ask what portion of it is reflected as temperature at any particular moment in time. The answer depends a bit on the speed of the gas molecules in relation to the speed of the piston face and on what time increment and size scale you want to observe the process.
The increased kinetic energy of these molecules can not propagate through the gas and away from the piston face at a speed any faster than the speed at which the molecules possessing it are themselves moving. Generally speaking, it is limited by the speed of sound in the gas. When the speed of the piston face approaches the speed of the gas molecules, very large gradients can build up creating supersonic shock waves.
Furthermore, the initial increase in kinetic energy is all oriented along the direction of the piston face movement. As these faster molecules collide at various and random angles with slower gas molecules, the slower molecules are sped up in random directions and the increase in kinetic energy is randomized. This energy is therefore re-partitioned among the three translational axes until the average energy in each axis is equal and relative uniformity is reached. Likewise, energy is also internally re-partitioned between molecular translation, rotation, and vibration energy storage modes within the molecule. This internal molecular re-partition is extremely fast - nano or pico seconds if I recall correctly. Now the increased molecular energy is clearly all thermal.
Bottom line, temperature and pressure gradients do occur on compression. For subsonic processes they can generally be ignored. These gradients are important in some cases. As one example, they form the basis for thermo-acoustic phenomenon. As another, they can form hot spots on objects traveling at supersonic speeds.