In parallel connection, potential difference across resistors remains the same.

Thermal energy released in resistor is given by $H=\frac{V^2}{R}\times t$

So, the ratio is $\frac{H_1}{H_2}=\frac{{\displaystyle \frac{V^{2}t}{R}}}{{\displaystyle \frac{V^{2}t}{3R}}}=\frac{3R}{R}=3:1$.