Lol you really need to look inside some phones if you think there's loads of air space inside large phones.
Also as we are talking about the SOC all your mysterious "stuff" is irrelevant unless you think the faster SOC needs more "stuff" as well.
So you stance is that scenario 2 is correct- large phones don't have any extra space, so it would be physically impossible to squeeze them into the smaller case of a small phone. Now you understand why smaller phones don't have the same specs, finally.
Also, the "stuff" isn't irrelevant at all. The "stuff" is everything needed to make the phone a phone. Cellular radio, antennae, battery, external connection interfaces, memory, flash storage, etc. The SOC needs that stuff, yes indeed. And in some cases, faster SOC needs "more", for example if you want to have the same overall battery life and you are switching to a faster but more power-hungry SOC, you need to increase the battery too.
But this is all besides the point isn't it? The question isn't will a smaller phone run hotter, but rather will a smaller phone run too hot?
...which brings us to the whole reason this thread was revived. The Nexus 4 was overheating in Anandtech's first round of tests. I think that is indisputable proof that, at least in some situations, modern cellphones can produce heat.
Phones are supposed to work in pretty crazy conditions sometimes, sitting in a car in a sunny day with no AC on for example, so I believe the manufacturers tend to play it safe and leave a large margin of error. So you probably could fit a full-size phone into a smaller case and get it working, but you wouldn't have the same safety margin.