Used to think the anvil just needed to be room temp for small stuff. Saw a guy at a demo try a cold weld on a big piece and it just would not stick, made a terrible mess. Totally changed how I see it. The heat gets sucked right out if the anvil is cold, kills your working time. Now I always make sure mine is at least warm to the touch before I even start. Makes a huge difference in getting a clean join.
You mentioned the anvil sucking heat out and killing working time. I actually find a cold anvil gives me more control, especially on smaller pieces. That quick heat loss lets me set the weld fast before I burn the metal. A warm anvil can make things too soft and hard to manage. I just work quicker and hit it harder on the first strike. It's a different way to do it but it works for me.