As long as inside your coop is dry, it doesn't really matter how much it's raining outside. Your chicks will not need a heat lamp, and putting one over them in a confined space where they couldn't get away from it could actually harm them if they got too warm. The main potential dangers are from your other birds and from predators. The behaviour of your other birds will likely depend a lot on where your broody stood in the pecking order beforehand, but even formerly timid birds can become fierce when protecting chicks. As for predators, try to ensure your coop is secure at night with no small holes that rats or weasels could sneak through.
