Many modern reed-valve 2-strokes have a rear boost-port running up from the intake port to the same height as the transfers. Once the piston uncovers the side transfer and rear boost port, the arriving low-pressure (vacuum) pulse from the exhaust draws air/fuel up into the combustion chamber. And with it, hopefully, some of the mixture from under the piston :-)
If the mixture under the piston is getting displaced with each stroke, there would be a cooling effect under the piston with each new air/fuel charge.