I don't think these rumours are related, personally - given my understanding of T239's thermal profile on 4N, 3.5TF would actually be a similar thermal profile to the original Nintendo Switch. There's also a bunch of technical hurdles to putting the fan in the dock (increased dock power consumption, for example), when you could just have one fan for all modes that speeds up when in TV Mode. I guess based on that, I should have expected it. I imagine that battery life will be better than the launch Switch not from reduced power consumption, which I now doubt, but solely increased battery density and size. We could see launch Switch thermals but still managing a V2-like battery life thanks to an improved battery.
I suspect a changed dock, if it is true, is for the following two reasons:
Product differentiation. To make it LOOK different.
Adjusted design to fit the LAN Port, and possibly others - the current Dock with LAN Port (OLED Model's) has a specific indent to fit a LAN cable, which was a design challenge as we know from the design inrwrviews. Building a design ground up with it in mind means that the dock would almost certainly need to be deeper from front to back. Additional size could also make room for an additional USB port, say two or three on the side and one on the rear. The Dock with LAN Port as it exists now sacrificed one of its USB ports to fit a LAN Port, a newly designed Dock wouldn't have to.
Unless it's some innovative but slightly nutty design relying on passive cooling in handheld mode, with a large fan in the dock for TV mode (as Oldpuck has rightfully pondered), I doubt we see a fan in the dock at all. I think a fan in the system is entirely reasonable, and having another fan pushing air through a tiny internal fan isn't going to help all that much, realistically, when you're better off just running that one small fan faster. Remember, again, that 3.5TF with T239 on 4N is, if I'm not mistaken, thermally similar to the original Nintendo Switch - it wouldn't NEED an additional fan, and if the new cooling system is better designed, it could achieve the same cooling with an even smaller or thinner fan.