The effective temperature of a star is relative to the fourth root of the luminosity and is contrariwise proportional to the square root of the radius.
L = k R² T⁴
If the radius remains continuous, while the luminosity doubles, the temperature must increase by a factor of the fourth root of two.
If L → 2L, then T → 1.189207115 T
So the answer is approximately 1.19 times.