I've seen a lot of recipes, particularly for things like quick breads, that call for combining melted butter with milk and eggs before mixing with dry ingredients.  Of course, if the milk and eggs are cool the melted butter will immediately solidify. Is there a technique for this that recipe writers are assuming I know? Or is it just intended that there be little droplets of solid butter suspended in the batter or dough? 
There are actually some recipes I've found that specifically call for adding melted butter to ice cold milk or buttermilk, intentionally creating little butter globs.   For example, in this America's Test Kitchen recipe for "Lighter Chicken and Dumplings" they do this.        FOR THE DUMPLINGS Whisk flour, baking soda, sugar, and salt in large bowl. Combine buttermilk and melted butter in medium bowl, stirring until butter forms small clumps; whisk in egg white. Add buttermilk mixture to dry ingredients and stir with rubber spatula until just incorporated and batter pulls away from sides of bowl.       If you watch the video, the reasoning is explained (starting at 3:20):     These little clumps of butter, once they are in the dough, they are going to melt in the dumplings and form little bursts of steam that are going to help the dumplings rise.   Now, while this may be an unusual method, the results will be similar in other applications. Because butter is partially water, when that water heats up, it turns into steam, which expands and creates airy space in the dough. With the dumplings, the effect is a nice, light dumpling that floats (as you would hope).   In general, however, as rumtscho pointed out in a comment, all ingredients should be room temperature unless otherwise instructed, so even after melting your butter, you will need to allow it to cool and allow your eggs and milk to come to room temperature. Doing so will prevent butter from forming clumps in recipes when they are unwanted. 