How can I warm bread making ingredients to room temperature?
To answer the question as stated: please don't use a microwave. You risk overdoing it. You don't want to cook your eggs or melt the butter. A water bath should work well. You can also set your oven to the lowest setting (should be around 50°C/120°F) and put them in it (no preheating), but then you must really check on them very frequently. Out of the two, I prefer the water bath. @Elendil's suggestion for a thermometer is also great. 

A side warning: I doubt that the dense bread is due to such small changes in ingredient temperature. You can easily start with cold ingredients, you just have to give the bread more time to rise. And kneading will easily raise the temperature of your dough from 65 to 85 °F. It is OK to warm the ingredients if you want to, but I suspect the problem is somewhere else, probably either in an incorrect raising/proofing process, or in a bad flour ratio (which could be due to a bad recipe or to measuring by volume instead of by weight).