Is the broth used to soak the pasta heated?

The point of the soaking is just to speed up the cooking time of the pasta. It will absorb water no matter what the temperature is- but warm water or broth will tend to absorb faster than cold. Given the time it is supposed to soak, I believe the recipe author used room temperature water/stock. Since you will be adding both pasta and soaking liquid to the cooking pot, and then cooking further until the pasta is al dente - it just won't really matter which you opt to use.