The lumps can cause problems if the butter is not evenly dispersed throughout the batter — some muffins can be oily while others are too dry. It’s always best to have your ingredients at room temperature before you mix them. This will reduce or eliminate the problem of the butter solidifying in your batter.
We have a favorite pancake recipe where we used to run into this problem. Our solution is to put the milk in a glass measuring cup and heat it in the microwave oven for a minute or so until it is room temperature or warmer. Then it does not shock the butter when we mix them in with the eggs and dry ingredients. In fact, we often pour the eggs into the milk and stir them together very well before putting the mixture into the microwave to warm. You can, of course, accomplish the same result in a saucepan over low heat, and people who are better at planning ahead can measure out the right amount of milk and leave it and the eggs out on the counter for a half hour or so.