Coldness and Fatigue

For the past several weeks I've been consistently cold - but only starting after about 3pm and lasting generally until I go to bed, at least for a few hours.  Usually I'm less cold if I'm moving around more, but usually during that time period I'm pretty inactive.  I've always had cold hands and feet, but when I start to feel completely cold it seems like my core temperature actually goes up.  Also, I feel more fatigued and weak, but I'm not sure if that's just because I don't sleep enough/drink enough water.  

Does anyone have any similar experiences/advice?  I know these are both symptoms of hypothyroidism, so if it's anything, I'm hoping it's that.  How fast does hypothyroidism tend to develop?