Left rear emergency brake sticks when its cold

LR emergency brake sticks when its cold. I have removed lr tire and unhooked emergency brake I then had the handle moved up and down inside car to make sure cable was not sticking it was free then I removed the spring and cleaned all the parts and sprayed with a lubricant, put it back together it seemed fine for a little while because it warmed up but as it got cold again it started sticking. Any help would be appreciated thank you. Paddy