Temperature Gradient 'flip'

Hello all,

I am working with a simple rectangular prism; made of copper. I am heating one face of it, and watching how the temperature changes in time. Once the temperature of the entire geometry is the same, the temperature gradient 'flips' So now the side that was being heated is cooler than the side that is an open boundary. That seems counter-intuitive to me. Mind you this temperature difference is within a degree.

Any thoughts as to why this is?

-Will