The tank in that link almost looks like the partition and back chambers is smoehow removable? (or was that just a pic before it was installed?). Whatever the case, that's an acrylic tank not glass.
To do acrylic in acrylic you would install it with weldon if you were to install it permenantly. That could be done, but would be pretty difficult to do nicely. The best way to do it would be to scratch build the tank and install the partition section during the initial build. The hard part about installing an acrylic partition in an acrylic tank that's already built is that the fit would have to be PERFECT, and even then it would be quite tricky to properly apply the weldon #4. If there were small imperfections they could be fixed with weldon #16, but this would get messy and ugly fast. Anything more than very slight imperfections would result in a partition that would leak, and or turn into a total mess.
That's a good suggestion about building an entire box and then installing that, might allow for some more wiggle room/imperfection on the install.
Also FWIW, when acrylic expands (or covers bow) it's not due to heat, it's the acrylic actually absorbing a tiny amount of water. Fully submerged acrylic parts such as sump baffles expand evenly. Acrylic covers will absorb more water on the wet side and this is what causes them to sag. The expansion is a tiny bit, bit in some cases has been enough to crack sumps that have tightly fit baffles.