My thoughts about burning off the thatch are not to do it. Here's some excerpts from this site with info on preventing and dealing with thatch in Bermudagrass. Do read the entire page as it offers lots of help.
Careful management is required to prevent thatch accumulation.
Bermudagrass does not tolerate poorly drained sites. On compacted sites and heavy clay soils, irrigation must be closely controlled to avoid waterlogged conditions. Hard, compacted sites can often be improved with respect to water penetration by core aeration and topdressing with sand or an aggregate material such as Turface. The presence of a heavy thatch layer will also interfere with water penetration. Thatch removal by vertical mowing and core aeration also improves water penetration and reduces the frequency of irrigation required.
Excessive nitrogen fertilization, beyond that required to maintain color and vigor, leads to increased mowing, irrigation, thatch control and pest problems all of which result in higher maintenance costs.
Without cultivation bermudagrass turf tends to develop thatch, grain and spongy conditions that result in scalping and a nonuniform appearance.
High nitrogen fertilization rates should be avoided during peak periods of disease attacks. Thatch should be controlled through proper mowing and cultivation. And, water should be applied properly to avoid severe drought stress or waterlogged conditions which increases the susceptibility of grass to some diseases.
Please note that I DO NOT recommend or endorse the herbicides suggested by the site.
The best time of year for thatch removal and core aeration is the fall. You can rent the equipment you need.
You may still have time to do this depending on the weather where you are.