Not necessarily, it depends on the amount of heat produced and whether you have a fan or not.
The fan would be used to blow air through the fins and basically blow the heat away - in this case, you'd need to have an area where air can be sucked in and blown out.
Without a fan, the air wouldn't move around a lot - not even if there's an opening. The cooling is (of course) a lot less than when using a fan.
The fins are simply there to increase the overall area where heat is in contact with air.
The air WILL still cool it, even inside the plastic case.
And as long as the air is cooler than the CPU, then it will work