G = H - TS
If T is high, G<0, meaning that a larger T makes '-TS' greater, so S must be positive (if it were negative then increasing temperature would make G more positive, but it makes it more negative)
If T is low, the temperature is not feasible, meaning G>0. So, assuming -TS is negative, for G to be positive H must also be positive (positive minus something small gives a positive).
I'm guessing you know how to explain why feasibility changes with temperature? When G < 0 its feasible etc. I think this is right.