Would 2000 millimeter wide exhaust ports cool as efficiently as a single 2 meter wide exhaust port? (more details in the post)

Assume we have a Very Hot Thing which needs to be cooled. Both exist in the middle of a sphere.

Option 1: A single 2 meter wide thermal exhaust port. The sphere has a radius of 80 kilometers.

Option 2: A lot of millimeter wide exhaust ports. For the sake of discussion let's say 2000. The sphere has a radius of 100 kilometers.

How many really small exhaust ports would it take to cool as efficiently as a single larger exhaust port? Would the extra 20 kilometers the heat has to travel, in such a small exhaust port make a difference? If 2,000 millimeter wide exhaust ports are not enough, what about 2,000,000 exhaust ports?

While typing this it occurred to me that I should know the temperature. I don't. Just assume that it is very hot and the same in both cases. Also, unfortunately option one is no longer an option due to security concerns but functioned fine for cooling.