Guidance requested: temporary stone or brick outdoor stove

I've seen lots of video clips of people making temporary outdoor "rocket stoves" by stacking cinder blocks. Can anyone recommend a good design and which type of block/brick/stone is best (something I can buy at Home Depot, including half sizes)? The objective is to burn scrap wood efficiently and radiate heat (cooking optional). Then I'll disassemble the whole unit when the warm season arrives. I have some cinder blocks lying around, but I suspect I can do better. I also have a few pieces of 6" stove pipe I could integrate into the design.

Bricks would be better. Regular concrete is a poor fit for flame contact areas.
The new cheapest bricks improvement stores will be always machine made - very dense. It would be better if you found some old, softer, hand made bricks for lower price than the new ones. Handmade bricks are usually more porous and porosity allows bricks to expand during heating.
Even cheaper,but more laborious would be to just build from your dirt (just remove the top organic rich layer).

If you have cinder blocks laying around, and won't need them for a permanent building project, I would just use those to make your temporary rocket stove. It will be very quick and easy. They will not last a long time, but should work at least for a season of burning scrap wood.

Old soft bricks would be better if you have them or can get them free or cheap. You can make mortar from clayey mud to stabilize a temporary brick rocket. It will not glue the bricks together, but will seal gaps and keep things steady.

If you have nice clayey subsoil, you can most assuredly make a rocket stove from that. A scrap wood inner form that you can burn out will work well, and mixing some straw into the clay will reinforce it. As long as it is isolated from damp ground (on rocks or concrete) and protected from rain, it will bake on the inside and start to become fired.

concrete does not withstand heat.

Not for long duration or high intensity, correct. The amount of heat from a small rocket stove will degrade the block over time, but they will last for a while, perhaps a season or two.

My mother had a fire ring backed by concrete blocks in a half-circle at her lake house, which over the course of a number of years' bonfires crumbled at the most exposed surfaces.