You don't really need a variac, you can rig up a lamp socket in series with a cord and fire it up with light bulbs for a limiter. I used to start with 60 W to look or smoke, then go up to 100W, 200W. Sometimes it's easier to put two sockets in parallel and the pair of them in series.
The great part about lamp bulbs is that they are quite idiot proof. If the load is a dead short, all that happens is that the lamps light
By the way I sometimes use this same idea when looking for a short in a 12V vehicle.
An isolation transformer, or at the least, "be very careful" is a good idea too, here's why:
Many older TV's don't use a power transformer, or may only "partially" use a transformer, sot that "straight line power" is into the TV circuitry on past the transformer. Some used "series wired" tube filaments, easily recogizable because of the odd tube numbers, or used only a filament transformer, and developed the higher operating voltage direct off the line.
THIS PUTS parts of the TV circuits and or chassis at line ground, and IF THE power plug becomes reversed, then the chassis is "HOT" with line power.
BE CAREFUL.
A "hot chassis" can also be "deadly" to your test equipment. With test equipment that is "3rd wire grounded" and you attempt to connect to one of these "hot" TVs, you WILL have a problem. Sparks, smoke, blown fuses, or damaged test equipment, TV, or "you."