Adding a material after heating

Hi all,

I have a 2D hemisphere that I want to heat up in air. The flat edge is heated with a constant power of 100W. After 60 seconds I would like to introduce a curved piece of copper on the curved edge. The heater still runs, but the copper starts at room temperature and so cools the hemisphere down, before heating up again. I am struggling with this, because I can't figure out how to introduce the copper at room temperature, because the initial expression starts t=0, and I need t=60. Does anyone know how to do this?

Thanks