Air cooling works well with almost all CPUs
I would say that the part where you need to be careful with is overclocking. You might not have any problems then as well. Most processors are built for air cooling anyways. I have tried to stress test my 8 core processor before with air cooling and I had no issues with temperature. Just make sure that the case fans are circulating the air in the case and that the vents are not being blocked (usually the larger case fans can keep a system very nice and cool and they work pretty quietly).
Also might be a good idea to ensure that the room is not hot. I found out many times that the room's temperature can affect the efficiency of air cooled systems which makes sense since the air used for cooling is the air around you but I am not saying to keep your room freezing temperatures like me unless you really like the cold.
Overall though I think that if you have a good heat sink and you have properly installed the thermal paste (used the good kind of thermal paste and not the cheep kind since this does affect the ability of the heat sink to draw heat away from the CPU) you should not have any problems. Just keep an eye out on the temps with something like speedfan or something.