The basic principles (underlying many variations and refinements) works as follows when extended by a thermal mass:

J-tube rocket mass heater in operation.
1. Vertically inserted wood burns sideways.
2. High temperature creates strong convective currents in the heat riser.
3. Exhaust gas exits sideways.
4. Heat exchange mass absorbs, stores, and radiates away heat.
5. Final exhaust is Carbon Dioxide and steam at low temperature (little to no elemental carbons).
Source: https://en.wikipedia.org/wiki/Rocket_mass_heater
The advantages for post-cataclymic survivors include:
- Reduced fuel to useful heat ratio (requires less fuel)
- Reduced fuel depletion (deforestation)
- Improved fuel renewability cycles (regrowth)
- Reduced fuel effort (cutting, splitting, transport, storage)
- Reduced fire tending (more sustained heat with reduced fluctuation)
- Reduced cooking/heating related time cost (freeing for other purposes)
- Reduced pollution (smoke, soot)
- Reduced health threats (injury exposure, fire danger, pulmonary and cardiovascular diseases)
Both rocket stoves and thermal mass back ends can be DIYed from natural and/or scavenged materials.
Dave Z