Derive the hottest spot on the probe's surface?

A space probe in the shape of an ellipsoid 4x^2 + y^2 + 4z^2 = 16 begins a spiral decline into the Earth's atmosphere. After an hour, the temperature at (x,y,z) on the probe's surface is T(x,y,z)= 8x^2 + 4yz - 16z +600. Derive the hottest spot on the probe's surface