These Buddy Burners show enough potential for me to experiment a little.
My successes and failures so far:
First tried out an empty chew can. Regrettably, I have an endless supply of these.

It is the perfect size for my purpose, as a heat source underneath a USGI canteen cup stove. It was a failure, though, as around the time I was getting a boil the plastic can started to melt and leak. Next up will be a Copenhagen can, maybe the cardboard walls will hold up better? We'll see.

Next I tried an Altoids and a cookie tin. I cut the cookie tin down with tin snips to about an inch and a quarter high.

They both burn well.

The failure on the Altoids tin is that once the wax starts to melt (as it burns) it leaks out the hinge holes on the back side. This could be prevented by only filling it to the height of these openings. I would pursue this idea further, but the lid prevents my stove from sitting flat over it.
The cookie tin burned well, but is too tall at 1 1/4". The canteen cup sets too low in the stove to sustain a good hot burn over the burner (chokes it off).
Just for fun I set the cup on the stove at an angle. I got the first bubbles at 6 minutes, but it took 19 minutes for a decent rolling boil. Granted, a lot of heat is escaping around the cup this way.

Here's some other universal things I've learned so far, if you plan on making one of these:
Underfill, rather than overfill these guys. Too much wax makes a candle, not a burner.
Use a bit of wick, slid down one of the cardboard holes, for lighting these up.
You don't need as much cardboard as you think. A little loose and sloppy is okay
Paul (111t) is absolutely right, these will soot up your pots quite a bit.
FYI, I left the cookie tin to burn, it died out after 1 hour & 15 minutes.