thick metal below a pot

Why would you want to do this?

They turn every pan into a cast iron pan, in terms of ability to remain hot after putting cold ingredients in them.
They help eliminate hotspots.
If you're doing multi-hour slow cooking, some stovetops — especially gas stovetops — aren't great at maintaining a steady low temperature. A diffuser will moderate the temperature, allowing all stovetops to do slow cooking and long-term simmering. It serves a similar role as a double-boiler, though it doesn't reduce the heat as much.

Some products you might consider:

Stryker Welding and Fabrication
heat diffuser plates
- copper heat diffuser [amazon] [ebay]
  - Duparquet
  - BellaCopper
  - Rachiele
  - TODO: Wouldn't the copper surface get lots of dents and dings, since it is a much softer material than the steel pans that will be moved around on it? Does it make sense to attach some steel sheet metal to the top? (whether by cladding or riveting)
- aluminum heat diffuser
I've seen people use a stovetop griddle (that typically straddle two burners) or a baking steel (possibly rectangular in shape so it can cover two burners), and using it as a surface that you can put multiple pots on.

There are two materials-science properties relevant here:

material	specific heat capacity (J/g°C)	thermal conductivity (W/m/k)	cost (USD/kg, wholesale)
copper	0.385	401	~$9
silicon carbide	0.670	270
aluminum	0.90	236 at 0°C	~$3000
graphite	0.708	168	$0.80
brass (30% Zn)	0.377 at 20°C	121
iron	0.442	70 at 25°C
carbon steel (1% C)	0.502	43
stainless steel	0.50	18

What size diffuser is good?

let's build this (Jan 2025)

Buy from this place, it seems like they'll charge a little less if there's enough cut-offs and scrap and such.

Stryker Welding and Fabrication
- materials they stock
- contact
Buy two 1/8" thick copper plates, a 1/4" aluminum plate, and if possible, two stainless steel sheet in the same shape, for the top and bottom. And maybe a short bit of copper rod, maybe 0.5" diameter, so I can make my own rivets?

Connect all the sheets together using countersunk rivets. Ideally the top and bottom surfaces would be entirely flush, to make cleaning easier.