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I think that there are other solutions too. One would be to have controlled burnings of areas of forest, to remove the layer of fuel on the ground. Another is to "high prune" trees (remove the lower branches), so that these lower limbs don't transfer the fire from the ground to the canopy.
In many ecosystems, forest fire is a benefit, and is a natural element of the forest cycle. You need to consider the species too. Some species like the Eucalypts have highly resinous leaves and bark, and go up like a torch. However, the main part of the tree survives and self-coppices. In California, some of the trees are very thickly barked as a fire protection. But the cones need fire in order to open and cast their seeds.
The problem (and it's only a problem as far as humans are concerned) is that forest fires are extremely hot and move very quickly - they are a kind of flash fire. There is a great deal of open structure, and preventing oxygen from getting in would be a real challenge.
I'm not familiar with thermobaric bombs or the area under which they are effective,
The overpressure within the detonation can reach 430 lbf/in² (3 MPa) and the temperature can be 4500 to 5400 °F (2500 to 3000 °C). Outside the cloud the blast wave travels at over 2 mi/s (3 km/s). Following the initial blast (compression) is a phase in which the pressure drops below atmospheric pressure (rarefaction) creating an airflow back to the center of the explosion strong enough to lift and throw a human. It draws in the unexploded burning fuel to create almost complete penetration of all non-airtight objects within the blast radius, which are then incinerated. Asphyxiation and internal damage can also occur to personnel outside the highest blast effect zone, e.g. in deeper tunnels, as a result of the blast wave, the heat, or the following air draw.
Blast radius is 450 feet (137.61m, 150 yards), though the massive shockwave created by the air burst is said to be able to destroy an area as large as nine city blocks.