My source is common sense, as well as being an Electronics Technician, as well as holding professional licenses for Commercial radio.
Your brother is being exactly what you say he is being. He radiates more heat than 2-100 watt bulbs do. What ever heat they produce is going to come from infra-red, as well as basic radiant heat. If the room were a sealed room that was air tight, as well as super insulated, those 2 lamps, on all the time, might make a slight difference in a day or 2. Since I doubt your house is that air tight, and well insulated, any difference is psychological in nature, and not from "real" heat the bulbs generate. Besides, their heat is going to stay near the ceiling, since hot air, rises. You might want to suggest that if he stays in one place, keeps quiet, and does absolutely nothing, except breathe, he would be a lot cooler. If he wants things to be cooler, invite him to go buy LED lamps. They are available, a bit pricey, but they do exist, and would seem to be a bit cooler. Personally, his keeping quiet is the best idea. If you want a demonstration, get a thermometer, him and some of his friends to go out and exercise, then put them in a relatively small room. Check the temperature with them before they go out, and then let them see what the temperature is once they return, and gather in the room. If it is small enough, you will see a temperature rise, from their body heat. You might also tell him to stay out of your room because he only adds to the heat in it.
Half a degree would not even be noticed, unless you had a really accurate thermometer. Feel free to tell him that I agree with you.