These are all very helpful comments, thank you!
I'm actually not using this in a PC. I have a self contained system, we had assumed since it had a heat sink and fan that it would be able to run independently. I have requirements that the environment of this card will be much hotter than 22C / room temperature. If it takes 4X 140mm fans to cool this at room temperature then it looks like we won't be able to use this.
Thanks again!