Through the researches I have made I have found that:
- fermenting non dried hay might result in self-combustion of the said
- hay fermenting dried hay can reach up to 60 C of temperature
- fermenting hay develops asphyxiating gases, like CO2 and methane
I'm not so sure that these are as big of a problem as you think. Starting a fire is bad but people know how to put out a fire. Getting to 60 C is bad if one is sleeping on it but not so much if used like a central campfire heat source in the "straw igloos" that others here proposed. CO2 building up is bad but humans evolved to know when this happens and with experience have learned how to deal with it.
A bit of extra CO2 isn't an "instant kill" and will wake people up. Assuming a reasonably healthy and able person is among the group in the "igloo" to watch the "fire" then they can all sleep in relative safety and comfort. Or as comfortably one might sleep in a building made of straw. If there's too much CO2 then open up some ventilation. If it gets too hot then stir it up to cool it down.
Are other means to get heat out of the question? Is the time and place on Earth within the last few million years? I ask because this can open up alternatives.
Every so often a fire from oil soaked rags makes the news, so everyone reading this should know that we can get heat from oil and plant material in the proper ratio. There's heat from this that is much like your proposed compost pile heated bed, and carries many of the same risks. I suspect that with experience people should be able to figure out a relatively safe means to get heat from oil and plant material without setting themselves on fire.
The oil for this heating can be animal, vegetable, or mineral. The "rags" can be most any plant material. Coal and charcoal can produce this same self heating effect as they are in many ways not all that different from oil soaked rags. Heating their homes from fire was ruled out but not fire for cooking. The same fuel used for cooking can be used as fuel for heating even if not burned. Oils produced for food, or collected from cooking meat, can be used for nighttime heating of beds without flames.
I ask if this is a setting on Earth in the last few million years because, geologically speaking, it was not that long ago when Earth was more radioactive than today. Geothermal vents and hot springs today are powered by radioactive decay deep in the core of Earth, on a younger Earth these vents and springs would be more common and more powerful than today. A nomadic tribe living where heat basically bubbles from the ground should be able to find ways to exploit it.
With naturally occurring uranium and water we cannot produce a self sustaining fission reaction. A billion or two years ago this happened naturally because the ratio of U-235 to U-238 was different then. https://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor
People on a "young Earth" where fuel for fission is far easier to obtain could build a pool type reactor without any real understanding of how or why it works. At first we'd expect them to merely exploit the natural reactors as they occur, then with time, and trial and error, learn to build and maintain their own. https://en.wikipedia.org/wiki/Swimming_pool_reactor
Because water is such a great radiation shield the risks of radiation from even a very primitive pool type reactor would be minimal. The people should learn not to swim in the pool or drink from it as that would result in bad outcomes quickly enough to equate contact with the radioactive material with the harm it does. I suspect the water would taste bad enough from the brew of fission products that people would not want to touch it, therefore preventing people from bathing in this radioactive water.
This kind of reactor left unattended would likely see the water needed to sustain the reaction boil and evaporate fairly quickly. Isotopes that "poison" the mix in a modern reactor, like xenon and iodine, would escape into the air and allow the fuel to last far longer in such a primitive reactor than in a modern reactor. To restart the reactor they could divert water into the reactor pool from some river or stream.
A nomadic tribe should be able to build a sod house or log cabin over a pool type reactor to contain the heat. This would take a lot of time and effort to build and so such a tribe would maintain these structures for a long time, coming back to them winter after winter for shelter. The tribe leaving the reactor dry and not operating gives time for the decay of more "fission poisons" that would prevent the reactor from sustaining fission, as well as giving time for most everything that could poison the tribe to decay away. The fuel will have a half-life in the millions or billions of years but the fission products will not, most of them will decay away in months.
Even without building a fission reactor there's heat that can be obtained from naturally occurring radioactive decay. Finding rocks and sands that produce enough decay heat to help hold back the cold winter can be done by looking for places where frost isn't forming when the air temperature is just below freezing. People could collect these rocks and use them to build a bed to sleep on.
Naturally occurring radioactive rocks will have isotopes with a half-life on the order of a hundred million years or a billion years. The rocks richest with these isotopes will be warmer to the touch than other rocks around them. These kinds of rocks won't be a fire hazard, or even a radiation hazard. Long lived isotopes decay predominately with alpha and beta radiation. Alpha radiation will not penetrate the skin. Beta radiation will not penetrate more than a few millimeters of rock. Sleeping on a bed of uranium or thorium sand is not going to be much of a health risk. Not a risk that a primitive nomadic tribe would likely notice as it would take years to develop a small chance of developing some effect. People have lived with naturally occurring radiation for as long as humans have been human, this means people developed means to defend against long term low levels of radiation.
The idea of what is basically paper towels soaked in bacon grease is far more feasible than my other ideas. I want to come back to it though so it's not lost among the lengthier descriptions of utilizing hot springs, a primitive nuclear reactor, or naturally occurring "hot rocks". I spent more time on the more complex heating because it's more complex. Oily rag heat is simple. If there's a potential in the setting for oil to bubble from the ground, or get squeezed out of sand or something, then this can be quite easily done.