Find some firebricks to block up the exhaust hole and that little fire will retain a lot more heat. Really, any forge is nothing more than a collection of insulation to contain the heat in one spot long enough for the smith to get the material to the temperature they wanted to get work on the material done. All you need is a smallish hole not much bigger than the steel you're putting in there.

I know smiths whose forges are great big piles of brick that get moved around and repiled frequently depending on the size and shape of the job they are doing.