A fresh air kit should not have any air exchange with the void above and below the fireplace opening for blower circulation, so this would not be how this air is entering. If it appears as though cold air is blowing up from underneath the burner pan because it disturbs the ember material below the logs, this is likely due to downdraft in your chimney system and not any outside air kit. If air were to be entering through the outside air kit while the log set is not being used and you have a barometric damper that automatically pulls in outside air when the combustion chamber is starved for oxygen, there would be more pressing issues as your home is under negative pressure. This may also result in the gas log set leaking carbon monoxide into the home while in operation, especially seeing as how the damper should have been either fully affixed open or removed with the installation of any vented gas log set. With the damper open and the house under negative pressure, air would then easily be pulled in through the chimney before any outside air kit as the open chimney would be the easiest point of access. If the damper was closed for use with a ventless log set, any barometric damper drawing in air while the logs are not in use would also be a sign of a home under negative pressure. If ventless logs were purchased to rectify an issue with downdraft causing smoke spillage while burning wood or cold air entering through the damper while the fireplace was not being used, then this is likely what is happening.
If this is a manually-operated outside air system, simply closing the outside air via the manual control would be a solution.
on January 8, 2018