25 years ago I helped my Dad buy his "last computer." He just turned 92 and celebrated by buying another one.
There are two cardinal rules in buying a computer. Rule 1: The day you buy it it will be obsolete because of the daily technical advances. Rule 2: Even if you buy a powerful machine, software programmers will work very hard to make you need more RAM, chip speed or a larger hard drive.
You are correct in your concern about laptop cooling, though multi-core processors do seem to run cooler. You can buy a cooling pad to help. (Or, as my son the computer engineer does, keep some large books in the freezer on which to set the laptop.) Most cooling pads run on AC or USB, so you have some portability when away from an electrical outlet.
The biggest problem with a laptop is you have limited expansion options. Since you don't like wires, you'll not care for the external hard drive you'll probably need for your photography. Also, since we're the same age, I imagine you'll wan a large monitor to supplement you laptop screen.
When I bought my last computer, I went through the same dilemma. I did not seriously consider an all-in-one because of the limited expansion, though I was intrigued by the laptop configuration with a detachable screen. Instead, with the price of decent machines being so reasonable, I opted for a desktop as my primary machine along with a laptop to take with me when traveling.
The modern processors are quad core and I'd opt for that, as well a 4GB of DDR3 RAM. (Hopefully the machine has expansion slots should you need more.) I bought a reasonably basic desktop that had open bays and room for expansion. To this I added a second hard drive and a better video card.
My best investment was to upgrade to a 24 inch LCD monitor that's easier on my aged eyes. I didn't throw away my old 21" monitor, but installed it as a second display. Sharing your love of wiring, I also installed a PCI wireless card that, through my wireless router, gives me access to both the internet and my printer.
The wireless card also gives me access, though a home LAN, to the laptop. That way I can transfer files from the laptop to my large desktop hard drive. When I'm traveling, There are several programs available to access my home computer from the laptop to transfer files, but I generally use a USB memory stick or online storage to keep my laptop storage at a reasonable level. (My son uses a 2.5 inch portable hard drive that runs with USB power to back up his laptop files.)
Conclusion: You can go, as I did, with two separate machines. (I got a discount buying them from the same company.) ...Or, if you want a single machine, I'd stick with the desktop and expand it with wireless, more hard drive and a really good monitor.