Can you use short branches or sticks instead of shredded wood?
Seems to me they would break things up.

Okay, lots of questions there....

Aeration...unless the contents are sopping wet, the action of tumbling usually keeps the material porous enough for aerobic composting. This would also be predicated on having enough air vents in the tumbler. What were you going to use as your Carbon material?

Heat...There will be some residual heat given off but there would be a ton of other considerations before I could say if it would heat your greenhouse to any kind warmth.

CO2...A tumbler is not likely to raise the CO2 to toxic levels, if it did, the actual composting would also decrease because of lack of O2.

Curing...once my tumblers have finished the heating phase, I transfer the contents to a curing bin. Tumblers excel at keeping compost materials well mixed and aerated so wasting that potential for curing does not make sense to me. I don't do worms but I would imagine they would love the stuff. I'd be careful using it as mulch myself until I was sure the toxicity was not a factor.

Lloyd

I'm actually planning on using the 'compost' from the compost tumbler on a 'no-dig' garden. I've been led to believe that you are okay using tumbler compost on a no-dig garden because you're not digging it into the soil itself, which is okay because it slowly composts before being slowly incorporated into the soil by the worms. Apparently using it this way avoids 'nitrogen robbery'.

Is this not the case?

Do I really need to finish it off by 'curing' it?

Oh, and I didn't realize you have to 'cure' your compost if using a tumbler. How do you do this?
I read that curing compost is done by stopping adding organic waste to the tumbler and turning it for 3 months. Is this true? If so that's a bit disappointing as I thought a tumbler allows you to make compost in a lot less time!

No, one does not necessarily have to cure compost if using a tumbler. People often get confused with when compost is ready to use. There are different variables and parameters and very often there are extenuating circumstances that come into play.

I cure my compost when it comes out of my tumblers (after high heat phase) because I want to be sure my compost will cause absolutely no harm for whatever it is used for and I can then re-load the tumblers for another batch.

The only way I can be certain of causing no harm is to ensure it is very mature. It is possible that compost straight out of a tumbler may still be toxic to some plants. There are a couple of simple home tests but I usually use the Solvita test myself.

The article Compost Microbiology and the Soil Food Web has some pretty decent explanations about why curing may be important.

A case of nitrogen deficiency will usually only occur when materials with a high C:N ratio are incorporated into a soil.

It is not always a simple concept.

Lloyd