Extrema of two variable function
You can take the differential with respect to X and Y to find that the extremum sit on the line y = X/2 and for the minimum and Y = 2x for the maximum. These increase with X and Y so the maximum sits on the point 5,2.5 and the minimum on the point 1.5,3
They will be 131.25 and 93.25 respectively giving a maximum temparature difference of 38.
PS. There might also be a clever way to formulate this problem as a lagrange multiplier, but I am not really sure if it is possible because of the complexity of setting the constraints to zero.
