Also,
You should edit your post to use the code button (upper left button). This makes the code more readable and copy and paste-able.
I would also change your NDSolve statement a bit:
soln = NDSolveValue[{pde, bc}, T, {x, 0, a}, {y, 0, b}, {t, 0, 10000}]
You can visualize it with something like:
ListAnimate@
Table[Plot3D[soln[t, x, y], {x, 0, a}, {y, 0, b},
PlotRange -> {Automatic, Automatic, {280, 350}}], {t, 0, 8000,
300}]