I said earlier that the 7805 got warm but not hot. That was true of my breadboard experiment. When I put one on the actual PCB, it was sometimes warm and sometimes really, really warm. I don't know what temperature it reached, but it was a bit uncomfortable to the touch. It was still possible to keep touching it with my finger indefinitely. I'm not sure how the 3D printed case will feel about that permanent source of heat after a few months.

I'm not sure why there was a difference on the breadboard compared to the PCB (it happens to be exactly the same 7805 device). I'm thinking about ways to reduce the ESP32 power draw (maybe by reducing the clock frequency or whatever other tricks I can come up with while staying in ESPHome), but I will probably add a heatsink to the BOM.

Meanwhile, I have been exploring homebrew heatsink stuff. Here is what I have found so far:

• The hole in the tab of the TO-220 package is 3.7mm +/- 0.1mm.
• 3.7mm +/- 0.1mm works out to 0.1417 to 0.1496 inches, or about mid-way between 9/64 and 5/32 inches.
• JEDEC (registration required) gives the dimensions in inches, min 0.139, max 0.161. 
• I don't know how closely manufacturers adhere to any of those specifications.
• I found that an M4 screw just barely fits into the devices that I have. It doesn't slide in and out, but it can be easily threaded into the hole. It's not snug enough that it doesn't need a nut.
• In North America, the standard screw for holding an electrical wall plate in place is size #6-32. The major diameter for #6-32 machine screws is 0.138 inches / 3.505mm. These are readily available in the US. I've got about 5 billion in various places in my junk box. Because of the way they are used, you usually find them without matching nuts, though the nuts are also readily available at any hardware store.

I was able to cobble together a makeshift heat sink using loose nuts and washers from the junk box. The only (tiny) challenge was finding a nut that was small enough in outer diameter to avoid the body of the TO-220. I wanted to insert the screw from the back side of the TO-220 so that any excess would point up and away from the ESP32 if I leaned the voltage regulator backwards to reduce its height, and also because any of the nuts and washers I used would also interfere with that body.

Here's a picture of my Frankenheatsink (M4 screw and nut, loose-fitting junk draw nuts and washers):

So far, it's staying just warm and not getting really, really warm.