Most 5.56mm-chambered AR's will run fine on Tula steel-case, and I'd expect most 5.56mm-chambered mini-14's would do the same. It's *possible* that a .223-chambered Match model might be a little more finicky, but if you have a Match model then you are probably shooting match loads anyway.
BillOfRights, I'm pretty sure the polymer used is one that won't melt at any temperatures encountered in a firearm. I haven't tried it, but I suspect the polymer would char and carbonize before it would melt; I may take a torch to a fired case just to see. Anyway, I've had zero issues with Tula and Wolf in my AR, shooting USPSA-style carbine matches; those aren't carbine-class round counts, but it definitely gets the gun hotter than slowfire plinking would, with no issues and no residue other than carbon.
I generally clean mine about every other match (mostly because I like to, not because it really needs it), and have never had a failure of any kind. Wolf/Tula does leave a little more carbon than PMC brass-case or domestic ammo, but still not all that much.
One thing about Tula/Wolf is that it is loaded a little milder than most brass-case .223/5.56mm, but mini's tend to err on the side of overgassing anyway, so they tend to work fine even with underpowered ammo.