Hi Ian and Fred,
I can see why Ian wants to do the barrel outside - one of the few cases where I'd consider that idea. It will lose a lot of heat that way; if possible I'd put a
shelter around it as you don't want the fire (or its keeper) drowning in the rain and snow. And there are lots of uses for a warm shelter.
As for exhaust - one of the common problems with these
heaters, especially in greenhouses where the orientation is pretty exposed, is that they do need a fairly conventional chimney exhaust (straight up through the greenhouse works great; patching in a piece of tin to cover where you remove the poylcarbonate is not terribly hard). Or they need some observant problem-solving about wind protection, and the exhaust as high up the building as you can get it. (In a warm bubble like a greenhouse or home, the air inside is trying to rise through any leaks or vents; and cool air is coming in down low to replace it. This means any hole down low becomes a
de facto air intake.)
Temperature once you've gone a few meters under a damp
garden bed should be pretty low, like 25 to 50 C, maybe 100 C if it's a super-short bed. I tend to prefer a metal exhaust chimney that can be 'primed' with another heat source if needed, but temperatures don't require stovepipe. Just make sure any exhaust is smooth, and the proper size.
I would not recommend using Portland cement for the stove; it will trap damp, and probably crack with thermal expansion. Refractory cement might work but you could still have the damp problem; and refractory clay or just plain clay-sand mortar works great when protected. I would put a roof over this area, allow about 3 feet (1 M) on each side of the hot barrel, and use it as a mud-room or drying room. About half your heat is going to come off that barrel; it might even be useful to enclose the 'furnace room' (with plenty of outside air ventilation) and use a fan to blow excess warm air either into the greenhouse or into the main house.
Yours,
Erica W