The #1 reason for make up air
Is if you have a naturally drafted B vent appliance like a water heater or open gas fireplace. The kitchen fan has the ability to backdraft carbon monoxide.
Our codes are pretty specific and I deal with make up air two ways. We MUST match the make up air to the exhaust, so in your case I would install a 600 cfm in-line fan and tie it into the exhaust control. If the air is ducted directly into the kitchen then we install an electric heater as Carnak said to temper the air.
We are doing another job where we are dumping the make-up air into a pantry, and as such is considered an "unoccupied area" and therefore does not need the air to be tempered. We must, however, install transfer grills to allow the air to move from the pantry into the kitchen which is adjacent.
Check local codes.:)