> Under those conditions, is my computer use essentially free?

It's 'free' when compared to an electric heater, but not when compared to a heat pump (e.g. a food refrigerator). Heat pumps can use their energy input to divert heat from a cool reservoir, in addition to simply creating additional heat.

So if you want to generate heat even more efficiently, keep a fridge in your room and fill it with water or soft drinks (water has a high thermal capacity).