There are a few ways to get the answer to this question. The most direct is to use the combined gas laws:
P1 * V1 / T1 = P2 * V2 / T2
Notice that you have two pressures, two volumes, and one temperature. Let T2 be your unknown temperature, the temperature at which the balloon has that maximum volume 450 cc at pressure 780 mm Hg.
P1 = 700 mm Hg, V1 = 390 cc, T1 = 20C + 273C = 293K.
P2 = 780 mm Hg, V2 = 450 cc, and T2 = T1 * (P2 / P1) * (V2 / V1) once you solve for T2 with a bit of algebra.
You can plug in the values and do the numbers.