To what temperature $($in $$C$)$ must a cylindrical rod of one metal $10\mathrm{.}069$ mm in diameter and a plate of second metal having a circular hole $9\mathrm{.}986$ mm in diameter have to be heated for the rod to just fit into the hole? Assume that the initial temperature is $27$C and that the linear expansion coefficient values for metals one and two are $4\mathrm{.}0$ x $10-6($C$)$ and $15$ x $106($C$)-,$ respectively.