Substrate is the media in which the mushroom mycellia grow and expand. Mushies are classified according to the substrate they grow on. Lignim (wood) or cellulose (plant).
I'm in THAILAND. Rice straw is used for cellulose, it is bulky and freely obtainable. In fact it is BURNED as a perceived problem causing some of the pollution that right now - as I type - limits visibility to about 800 meters. It is my choice of substrate - I'm surrounded by it, might as well do something with it. Grow food and reduce pollution in one go - AND make
compost from the spent substrate. Some experimentation has revealed ANY organic matter is good for some mushroom species - bamboo leaves - very think on the ground under groves, corn cobs insides after the corn kernels have been removed. Lots of waste stream sources.
In effect heating at least 200 litres of water is required. Possibly up to 400 litres depending on quantity of substrate to be processed.
BURNING as explained in the OP is what I don't want to do. However i may be forced to .... I can pre-heat just in a simple glass encased black poly tube up to 50c ... from there to 90c will take more energy perhaps from charcoal as suggested. 5 hours is untenable with an open burn - tending a fire that long is not on. However insulating and using electricity on a thermostat may be viable to maintain the temperature.
I did have an interest in using Fresnel lens as concentrator - and accept that it would need to be repositioned every half hour to maximise effectiveness. Perhaps it could be a supplemental heat source using just a little electricity to top up and keep constant.
Your ideas are welcome.