This excuse is your perfect opportunity to go buy some new tools!
You will need a Tig welding machine and a bottle of Argon gas. If the case is Aluminum then it'll need to be a Tig machine capable of AC. Be aware that if you get one with high frequency start, that all electronic components should be kept far away or the RF can fry them. Mig could be used (with spoolgun for aluminum) if you don't mind grinding away at the resulting huge blob of weld afterwards.
Once the hole is made suitably smaller, you will need to drill and tap the hole with new threads. Far and away the most common computer screws are #6-32 UNC (the coarse thread one) or metric M3 (the fine thread one). Such a repair would be as strong as stock. Alternately you could tack weld a nut inside the case if there's room for that, which would result in a repair far stronger than stock.
If you don't mind a repair that may not be as strong as before, those aluminum brazing rods (for use with a propane torch) or punkncat's suggestion of just gluing the nut behind the hole may suffice (you can grind away part of the nut if needed for clearance, or use a rivnut/nutsert). Heck, you could even use a punch/ball-peen hammer or locking pliers to shrink the hole slightly, or drill another hole right next to the screw hole and and pry towards it (both methods will displace some metal toward the hole so the screw can catch).
Or if you don't mind a non-matching thumbscrew, just find one with larger threads.