Soap does not have to be heated or even covered/insulated to get hot enough to go into gel. You might need to cover it or warm it -- experience will tell you this -- but not necessarily.
Most of the year, I only cover my molds with waxed paper mainly to keep the dust off, but I'm sure it holds in a bit of warmth. Most of the time the soap gels. In the winter when my home is cool -- in the mid to upper 60s F -- I will put a box over the mold to hold a bit more heat in. I almost never use techniques like insulated box, heating pad, CPOP method, etc. to force gel. If a batch doesn't fully gel, I'll CPOP after the soap is done to fix that, but I seldom have to do that even.
The gel temperature varies depending on the fats used and the water content in the soap. For any given recipe, higher water content => lower gel temp and vice versa. Having never measured the gel temperature myself, I can't say what's typical for my soap. But Kevin Dunn did a study of water content and did measure the gel temperature of his particular "Duck" recipe. It varied anywhere from about 140 F (Duck recipe with more water) to 180 F (same recipe with less water).
If you do choose to heat the soap with a CPOP method (oven heating), the oven does not have to be at the gel temperature of the soap. It only needs to supply sufficient extra heat to ensure the cooler ends and edges of the soap get warm enough to gel. The center of the soap will get hot enough all on its own to gel.
You don't want the soap to get any hotter than absolutely necessary -- excess heat causes problems too. That's why people these days often heat their oven to 110-120 F rather than the 170 F temp that was recommended some years ago.
"... The fact that my soap is now 5 hours in and still feeling warm, is this heat the gel-phase in action? ..."
Not necessarily. When the sides of your mold are warm to the touch, that is definitely a sign that saponification is happening, that's for sure. But that doesn't 100% mean it has gotten hot enough to go into gel.
As you can see from Dunn's results, the soap has to get pretty toasty before it goes into gel. If the sides and bottom of my wood molds are on the edge of being too warm to hold comfortably, I'm pretty sure the soap is in gel.
I can sometimes see when the soap is in gel when there's a darker oval in the center of the mold. I have to say that darker oval isn't always super obvious to me for some reason.
In those cases, if I'm feeling especially curious, I will gently press the top of the soap (with a gloved finger) to see if the center is markedly softer than the edges. That center softness surrounded by firmer edges is another sign of gel, although at the risk of messing up a little spot on the top by me poking around.