Electronic – Is DC heating faster than AC heating

Two subjects are covered here. First, reality. Second, the questions posed.

First, Reality : About the most you can get from a U.S. 120 volt plug in is 1500 watts (generally speaking). So your heater element will draw more current (because of lower resistance) until the nichrome element heats up. During this transition time, one depends upon the circuit breaker characteristics to not shut off (trip off). Then, counting upon your forced air cooling (fan), the nichrome element should stabilize (temperature wise) at 9.6 ohms. That is as good as it gets for a constant applied voltage.

Second, your question : "How do I figure out the cold resistance". You need to get the manufacturer to supply you with the expected operating temperature where the resistance is 9.6 ohm ( or rather, at what temperature will the nichrome be at 1500 watts). From there, you can use the nichrome's temperature coefficient to calculate the resistance at room temperature.

First, I'd recommend looking into Cotronics' various epoxy and/or ceramic supplies for coating your Nichrome wiring and sealing it. I don't know what temperatures you expect, but it's something to look into. They support quite a range. Of course, I've no idea what you are really doing here. So I don't know if this suggestion will be at all useful. But there it is.

Second, you may need a way to monitor the temperature. It's unusual to operate Nichrome heating elements without some kind of temperature feedback so that you can achieve some desired level of temperature control. You could observe this temperature and get an idea if it is "red hot" enough, then. How you do that will depend on the exact range and/or why you are seeking such a temperature.

Also, keep in mind that the shape of your object and the materials used and a host of other factors will affect the color appearance of it. You can take a block of aluminum, drill a small, deep hole into one side of it, and heat it up to a certain temperature. The hole will appear "red hot" while the rest of the block doesn't even show color, at all, to your eye. And if I used copper, it would be all different besides. This idea of "red hot" is vague and poorly expressed in your question.

Finally, I think the idea of a relay is fine enough. Resistive loads like this are pretty tolerant of different methods of control. You could consider solid state relays (SSRs), too, though those will have a voltage drop across them which makes them dissipate power and possibly require heat sinking.

I can't suggest any better guidance without knowing a lot more about what you are doing, and why you are doing it.