Oooh, nice.. it's either a 'Classic Core' or an SC1, not really able to tell from the outside. I'm guessing SC1 since we made 10 times more of those than the CC. The CC was basically only made during the first year or two of UD.
I'd say that's fairly standard size for a Twig.
Hotter to the touch yes, but a tiny bit cooler in the core and for hits.
Softer woods act more like insulation and trap more heat inside whereas the harder/denser woods tend to transfer more to the exterior of the wood and radiate it off like a heatsink. The thinner the body the hotter it will feel in the hand (for all densities of wood).