I see what you want to do. You want to be able to "draw" on the wall.
Unfortunately, with most any handheld laser, you're going to have some problems.
1. Even the most powerful 1000mW on up handhelds have a hard time heating/burning at any great distance, because it's very difficult to hold it still long enough, or move it in a steady slow line to heat or burn anything. The shaking keeps the spot moving and it won't heat/burn reliably.
2. The most powerful lasers that are reasonably priced will be visible blue 1000mW+ 445nm lasers, or IR lasers that can be 1000-2000mW. The problem is that they tend to have wider divergence, and no matter how carefully you focus, may not get a hot spot at more than maybe a dozen feet.
And the IR laser in that power range is insanely dangerous, since you can't see the beam, and it's way, way, above the threshold to do eye-damage, which can be as little as 15-20mW.
3. Even if you do get a warm enough spot, can focus it right, and hold it slow and steady enough to draw on the thermochromic paint, the line between heating and simply burning the paint will be a very fine one indeed.
4. DPSS green 532nm lasers generally have tighter beams with lower divergence, but getting one that's powerful enough to reliably draw on your wall will be well over $500, maybe even $1000... or more.
What I think you should consider is getting glow in the dark paint, and getting a "Blue Ray" (violet) 405nm diode pointer. It will draw on GITD paint amazingly well. The short wavelength violet beam, even at a modest power like 10-20mW will make trails on the GITD paint so bright you can see them even with room lights on. Maybe even sunlight.
And you'll be able to do other cool stuff like make shadows with spotlights, stand in front of it setting off a strobe light etc. Jump in the air right during the flash etc.
Here's an example of what I'm talking about:
SolarColorDust.com Canvas Painted with Glow Dust for Laser Drawing - YouTube
I think this is an ad or demonstration for a high-end very strong GITD powder, but even Rust-O-Leum GITD paint is often sold in hardware stores (Home Depot & Lowe's if you're in the USA)
Also, instead of heat, there are also photochromic powders/paints you can use too, which will leave dark purple trails when exposed to UV, or near-UV 405nm laser light.
Here's an example of that:
SolarColorDust.com Canvas Painted with SCD for Laser Drawing - YouTube
Simply put, a laser won't always deliver HEAT reliably to make a physical change that relies on temperature, but they will always reliably deliver LIGHT to create changes that need light energy to drive them.
