Depending on the design, isn't there some chance that the heat could detonate the conventional explosive used to force the nuclear material together? as far as I understand it, there is definitely a risk of detonation, though it's hopefully very low. Physics is not directly the reason for it being so low either, but more safeguards put in place to ensure detonation only happens when it's supposed to and is prevented otherwise.
Most high explosives will not detonate when burnt. They need to have a shock wave running through them for the detonation to occur. The initial shock wave is usually created using a detonator, which uses a very small amount of a much more risky explosive.
You can get a lump of C-4, and use it as fuel for a fire to cook over without any danger, and in fact soldiers certainly used to do this. You can also hit it with a hammer - the shock wave caused by this isn't strong enough to cause a detonation.
In terms of a nuke, you need to detonate a set of independent lumps of explosive with very precise timing, in order to get a compression lens that will squash the fissile core sufficiently to get a nuclear explosion. Heat is unlikely to cause this to happen with a sensibly-designed bomb.
It's still very dangerous if the high explosives go if in an uncoordinated way. And then you have kilograms of enriched radioactive material spread all over. Not as bad as a supercritical reaction, but enough to worry about.
Uranium isn't really that radioactive. U-235 has a half life on the order of 10^9 years. It is only when uranium is brought together into supercritical lumps that it becomes a problem from a radiation point of view. However, it is also a toxic heavy metal, like lead, and that is a problem. That hasn't stopped militaries firing lumps of it around warzones the world over.
If I understood this correctly, the main challenge in nuclear bomb design is to time the conventional explosions in such a way that the resulting blast will compress the nuclear material, achieving critical mass, and not simply tearing it all apart.
So I think that this fire would probably not have caused a nuclear explosion.
Years of testing have never yielded a nuclear detonation from the conventional explosives cooking off in a warhead - radioactive strewn desert in Australia is a testament to the British testing this directly.
Nuclear bombs require absurd - something on the order of microseconds (I suspect nanoseconds probably come into play) detonation precision in order to reach super-criticality.
