I have the same problem...
Like a 60 cycle hum... My problem is, I didnt use a wire nut, nor, solder the wires, (to me its the best connection, but my girl busted my cold-heat the first day I used it..sheesh, she dropped it, so I have to order a new one, once I get that, I will solder the wires and see if that stops it).
Mine is a new fan also, so, its not like its got a lot of wear.. so, I will wait another month to get that and find out...(this drives me nuts cause its in my bedroom!!).
I actually wondered if it maybe out of balanced, but, this is a six blade fan 25 inches from tip to tip..(very small fan), so, I wll try this, and if you find out let me know, will ya? Thanks.