generally fires burn fast and hot. even so only some seeds survive-usually those which in fact need fire to germinate. after the 90's yellowstone fires aspens sprouted everywhere whereas formerly aspen from seed was very unusual. it is the long exposure to damp heat(140-165) which kills seeds in a hot compost heap.

It is not the same Klem. As a retired wildland firefighter of many years, here is my take.

When grasslands burn, the seeds which survive are in the top layer of the soil. It usually does not get very hot below the surface, or for only a very short duration. Most of heat will rise away by convection. You can place your bare hand on the soil a few feet behind an advancing flame front in grass.

Some forest fires in heavy fuels will burn very hot for longer durations. This can temporarily 'sterilize' the soil of most seeds. Certain trees are 'fire species' and require heat to open and germinate.

Hope this helps

Stating that composting temperatures will kill weed seeds is too simplistic since there are many factors that will influence that. Plant species, moisture content of the seed, whether the temperature where the seed is actually gets hot enough are all things that need to be taken into consideration.
Then, there is some research that appears to indicate that it is not the heat of composting that kills the seeds but that the seeds germinate and do not find the sun they need to grow and so die.