Hey, ya gotta find your fun where-ever you can.
W/cm square... watts?
Yep! So if your heat shield has to survive a peak heating rate of 1,300 Watts/cm^2, it's like aiming a 1,300 Watt hair dryer on each square centimeter of the heat shield surface.
What they generally do for testing is to hit the heat shield material with a plasma arc, sort of like what you'd find in a welding shop. I'm not sure how good a job a propane torch would do, but it would be a similar testing concept.
The other parameter is the total heat soak, which is in Joules (a Joule is one Watt for one second) per square centimeter. Your shield might survive a brief period at 1,300 Watts/cm^2 but erode away before re-entry was completed, so you have to check the total energy the shield can take. For example, one minute (60 seconds) at 1,000 W/cm^2 would be 60,000 Joules/cm^2. In older units common to NASA's early days, they'd have expressed this in BTU's/square inch.
So to test a heat shield material, you take a block of it and heat it with a torch, starting the burner on low, then cranking it up to eleven, then slowly backing off to simmer. As the heat soaks into the shield material the shield could start to melt internally or it might crack, both of which would be very bad.
For some applications you might just use a heatsink material, like a thick titanium skin which will heat up as you re-enter. The test there would be to hit it with the simulating heating it would experience and make sure its temperature never exceeds your design limits. For the Shuttle, the idea was that the tiles should never let the aluminum skin of the shuttle get too hot.
There are lots of links online that show pictures from testing the Apollo heat shield, where you can see the ablation and burning in various test blocks they tried out.