Cooling Tower Efficiency

Unless the airflow is restricted, then there will be very little effect. The performance of a cooling tower has a lot to do with the difference between the air's dry bulb and wet bulb temperatures.

Is this a dry fluid cooler, or a wet cooling tower? If it is wet then you may have problems with moisture condensing on the underside of the roof, and other obvious problems affecting the semi-enclosed environment. I can also see problems with recirculation which will reduce efficiency.

Perhaps a better design would be to duct the discharge to atmosphere. Also, being an extrusion plant the ambient air would likely be hotter than the uncovered outside, so the efficiency of the cooling tower will be affected by the air temperature under the enclosure. Some things to consider.

Good point. The original poster needs to be aware that running a wet cooling tower is a hazardous business and that steps need to be taken to prevent the spread of the legionella pneumophilla bacterium.

Thank you for the excellent orientation. As the fluid to cool is going to be water, it definetely cannot be a dry fluid cooler, but a wet one.
So, according to your comment, a duct to discharge the moisture to atmosphere should be considered as well as a good ventilation system to keep low the air temperature under the enclosure.