It sounds like hyperthyroidism might indeed be the cause and I'm glad you're going for a test to find out for sure.
Just in case it's not that, I don't know if this applies at all...buuut.
I have heard (but have never verified) that sometimes pets have weird seasonal shedding reactions based on our modern houses being heated and air conditioned versus the temperature outdoors. basically they go out and they are hot then they come in and it's 'un-naturally' cold. I admit this is total speculation but I thought I'd throw it out just in case it might make sense in your case.