So it hasn't been working out too well. Running off of the floor fan and no A/C, the room still closely mirrors the outside. It was making some difference, but not enough. Yesterday, I turned the exhaust fan down to low (instead of high) as an experiment. Initially, I had the exhaust fans on super-high, hoping to suck as much hot air out of the room as possible. I'm now going with a low exhaust speed with an idea that maybe that air I'm pumping into the room from the basement needs to stay in the room longer. Today, with a temperature of 84F outside (in the shade), the room is holding around 78F inside. So, that is some improvement.
I also believe i need to pump *more* air from the basement into the server room. Before I rush out and purchase a bigger fan, I am trying a cheaper experiment - removing the filter from underneath the fan. If that helps, I will look at different filters to see what provides the highest air flow.
Despite the ineffectiveness in the server room, some floor fans could still do a good job in other rooms of the house -- they don't have as many "heaters" running all 24x7 during the summer.
I maybe assuming, but a bigger exhaust fan maybe in order or else a new A/C. Also, don't "professionals" just use A/C's for their server rooms?