To cool an enclosed unit you need to move enough cool air in and warm air out to keep the heat source for gaining on you. Moving air around inside a cabinet will not do the job, and may actually add to the heat load by the amount of wattage consumed by the fan itself.

If you are going to move air through the grill cloth you can expect it to get dusty over time. Drilling holes may or may not help, depending on where they are drilled. Keep in mind that heat wants to rise, so see if you can arrange a cool air intake below the heat source and a warm air exit above. Without both of these you will just have the same trapped bubble of warm air you have now. Small holes mean you need a fan's help, large holes (read: very large) mean you may be able to count soley on convection.