There's no need to visit the dealer, swapping out that relay module was easier/faster than changing a tire. Even knowing that some reprogramming was done to alter fan speeds, I suspect that's all in the main computer, whatever Ford calls it. Out of curiosity I cracked open the old module and it's got small circuit card in it, but I doubt the 'reprogramming' changes the firmware in that box. I think it's more likely that they just change the commands/signaling that is sent to it from the main ECU.
The service coordinator at the dealership helped me out by giving me the part number for the whole assembly: ba8z8c607c. From looking at various ones for sale online, there may be a different one if you have the tow package (mine didn't) or a build date after ~10/2011. In the end, I don't think the relay assembly is different, they all end up being called Motorcraft RF273.
If the fans don't spin, that box isn't doing you any good anyway so just take it out so you can compare part numbers and hunt online. I wouldn't buy they whole fan/shroud/relay package like I did, just replace that silver box if you can. If it's unavailable to buy separately, you can get the whole shooting match off RockAuto cheaper than anywhere else.
In theory, changing out the shroud assembly isn't difficult but it looked to me that it'd slide out the bottom easier than lifting it up, but you may end up having to disconnect one or both radiator hoses either way. I wasn't looking forward to putting it up on stands or driving to a friend's house with a lift. That shroud is over 20" tall, so lifting it out might be easier if you don't have access to a lift.
Bottom line, if they don't spin with the AC on max I'd suspect the relay module. Test your fans with a couple jumper wires to their plugs and if they spin I'd pull the relay module then find the easiest, cheapest way to replace it. I suspect you can drive with it out since my Explorer's computer didn't know it was blown anyway (for months likely).
After I replaced mine the car fired up, reset Sync (because the battery was disconnected) and once I hit max AC I knew the dealer wasn't going to get $800 out of me.
Good luck, here's a pic of the old and new relay module (everything on the labels is identical). Maybe the part numbers will help someone out. It's installed upside down from what's shown below. Disconnect the three connectors and use a torx bit to remove the one screw holding it in, tilt it down and lift it out.