Sounds like an interesting experiment! I use mediums, so I don’t wire.
Looking on the current ratings for 26 gauge copper wire, it looks rated for about 2.2 amps, and 0.04 Ohm/foot. Obviously steel is not as good of a conductor as copper, so it will heat up sooner, but my guess would be you’ll need around 5amps to get the wire warm.
Technically speaking the heat output from the wire = P = VI = I*I*R. I really have no idea what the resistance of frame wire becomes when it gets hot. That is a big unknown that radically changes the calculations that follow. Let me just guess 1 ohm and see what the numbers say.
To melt wax, you probably need the wire to generate about 20 watts of heat. We now have enough data to run the calculations
P = IV = R*I*I
20watts = 1 Ohm* I*I. Solving for I we get 4.4 amps.
Getting 4+ amps out of a transformer will not usually be your most cost effective approach. When you need more that a couple of amps, the most cost effective power source is an old (or new) computer power supply. They can output a good 30amps at 12VDC is you need it.
If you use a 12volt output from the supply, at 4.4amps, you’ll drop 4.4volts over the 1.0 Ohm (?) frame wire which means you would need to drop the remaining 7.6 volts over a current limiting resistor. However 7.6V x 4.4amps = 33watts. You would need a current limiting resistor rated for 33 watts. That is completely impractical.
Computer power supplies also have 5volt and 3.3volt outputs you could try. These are typically good to 20amps. IF the resistance of the wire does go all the way up to 1 Ohm when hot, then a direct short to the 3.3v supply would flow 3.3amps and deliver 10 watts of heat to the wire. That MIGHT work IF the resistance of the embedding wire goes up to 1 Ohm. If the resistance is less than 1 Ohm, this sucker is going to get RED hot without a current limiting solution.
IF a direct short to the 3.3volt supply half works, but doesn’t give you enough heat, you might a direct short to 5volts.
Really the BEST solution and the most controlled solution is to PWM your power going into the wire. This allows you to deliver the exact current into the wire you want. You don’t have to worry about dropping voltage over a current limiting resistor in this case. I would get a nFET rated at 10 to 20amps and PWM your 5volts thru the FET and into the wire for a nice controlled heating solution.
ALWAYS remember fooling with electricity is DEADLY dangerous. It only requires 50mA to stop your heart. Always follow good electrical safety habits.