If by cooling system you mean the cooling fan, it takes a while for the coolant temperature to rise enough to trigger the temperature sensor that activates the fan. This is to help warm up the engine and to avoid unnecessary operation of the cooling fan when it is not needed.
check fuse for cooling fan, or possibly temperature sensor at inlet.
It takes a moment for the cooling system to kick in and start cooling. So the warm air that is sitting in the system is forced out when the unit is turned on.
The CRV has a very efficient cooling system and the fans only come on as necessary to assist cooling. When you engage the A/C they usually kick on for a minute or two to maintain coolant temperature and will kick back off if they are not needed. So, if you are not overheating you probably don't have anything to worry about. If you are overheating you probably have a bad fan relay.
The cooling fan may not kick when the car heats up due to dirty filters. Another reason can be a bad air pocket around the thermostat.
This engine and cooling system fan on 210 F. and stabilize at 195 degree.... 210 on a hot summer day.... with a 180 thermostat
it usually turns on around 200 degrees
mine kick on around 230 temp.
One kicks on for normal cooling, they both kick on when the air conditioner is turned on.
my fans on my 95 sls come on at 223 degrees. Larry Venice, Florida.
I believe that the fan(s) come on automatically with the AC system. Someone else might be able to confirm that. If so, then I would guess that you need to find and replace the temp sensor/switch for the fans.
Because its probably not working. Try turning on the AC to see if they both kick on and make sure to do this when the car is warm. If the car is cold they fans wont kick in.
The A/C is supposed to cycle on and off and this is normal. If however it is cycling on and off very quickly or seems to not be cooling as it should, it more than likely has a leak and is low of refrigerant. Take it to a professional, have the leak repaired, and the system recharged.