Hmm... Okay. Are we talking electric fan, or belt-driven (not too familiar on the grands...)
If electric... I don't think it's a variable drive fan, should only be two speeds: on or off. To the best of my knowledge, that is. My Jeep was vibrating and making a hell of an awful noise until I realized that the electric fan had mud caked on it. See, this fan does not run all the time, only when it needs to to help cool the engine, so the mud has a chance to dry on only one side, causing a vibration... Make sure this fan is clean inside and out, any little amount of mud on a single blade will throw it off balance causing a noise and vibration...
If it's your mechanical, belt-driven fan that's the problem, it sounds like your fan clutch. This is a creature that basically disconnects the fan from the belt drive as needed... See, when the engine is cold, the fan doesn't need to be spinning like crazy. The engine spinning the fan just happens to put more load on it, causing slightly lower gas mileage, not to mention that if the fan was constantly spinning hard and fast, the engine would not get up to operating temperature in a timely manner, again, fuel economy issues... There is a little bi-metallic spring inside, just like a coil thermometer. As the fan clutch gets hotter, the spring expands, tightening up the grip between the drive, and the fan itself, causing the fan to spin faster with the engine... With the engine OFF, and the keys OUT of the igntion, spin the fan by hand, think Price is Right. If it just spins really freely, little to no resistance, your fan clutch is shot. If it is difficult to spin, or feels rough, like there's sand or something in the drive, your clutch is seizing/seized, either way, needs to be replaced... The fan should turn a little and come to a halt, tangible tension on the drive, it's pretty easy to tell the difference between a free spin and what it should do...
Regarding the mud... Up here, we have nice fine sandy mud in the place I go wheeling... I put the hose to the radiator every day, and still got mud out of it... Chances are, you have not gotten it all out yet, keep on rinsing it every now and again, front and back... Powerwashing is, unfortunately, not the best idea, though it makes things SO much easier, it can also bend up the fins in the radiator, making things worse... As I understand it, holding a hose, no nozzle, to the radiator surface and letting the water come out the other end, and working it that way, top to bottom, is the preferred method... Mud is a pain in the radiator, there are a lot of very small holes in it that like mud very much. It was about a year before I was finally confident that the temperature issue was gone, a thermostat, a radiator flush, and who knows how many gallons of water later...
Best of luck, hope some of this helps.
