If your heater is to be directly mains-powered you might be better off to buy a commercial heater as it will be properly designed and insulated. Popular types are band, strip, cartridge and calrod.
You can design the heater take whatever current you happen to have available using a given resistance of wire, however the length of wire will be fixed at something that is probably inconvenient, and the voltage may not match what you have available.
For example, if you design it for 1A you will need 65 ohms (and 65V), which is 65\$\Omega\$/8.286m\$\Omega\$/m = 7.8km of AWG14 wire. Not very practical.
If you design it for 12V power, you would need 5.4A and more like 260m of wire (still a lot).
At 3.3V you would have 20A but you'd still need 20m of wire. That's about the lowest voltage supply cheaply available (within the range of a 500W ATX supply).
That is one reason why heaters are normally made with nichrome, Kanthal or other high-resistance (and refractory) alloys.
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.
Best Answer
The hob power is typically controlled using a thermo-mechanical duty-cycle controller.
Figure 1. Part of a hob power regulator.
There are three parts to the control.
Normal operation:
This type of control is on-off control with adjustable duty-cycle (the percentage of time the power is on). It works well for a cooker as the thermal mass of the hob, pots and pans is generally high enough that a 10 s blast of heat won't cause too rapid a fluctuation in temperature.
Note that this type of control has no idea of what's actually on the hob or even if the hob is connected! It does not control the pot temperature - only the power fed to the hob - and really it's only an adjustable duty-cycle timer. So, for a given setting a small pot will get much hotter than a wide frying pan that can radiate the heat. Power setting is determined by the cook using his/her experience.
You are right that a variable resistor would get very hot. At half-power it would be dissipating as much power as the hob itself. The on-off control is much more efficient and uses hardly any power.
Note that this pulse technique can be used at very high frequency to dim lights or speed control a motor. In such applications we refer to it as pulse-width modulation. The frequency of the pulses is chosen, for example, so that in the case of lighting there is no visible flicker or, in the case of a motor, that it doesn't cause vibration.
Figure 2. A PWM signal giving 80% power, 20%, 80% and zero power.
Bimetallic strip
Figure 3. A bimetallic strip consists of two dissimilar metals of different coefficient of expansion bonded together. As temperature rises the strip will turn convex on the side with the metal of higher expansion rate.
Oven thermostats
Figure 4. The oven thermostat has a fluid-filled remote bulb and capillary tube. Expansion of the fluid in the bulb drives fluid up to the thermostat where a bellows actuates the contact. Rotating the knob adjusts the distance of the contact from the actuator and thus the temperature at which it opens.
Simple stepped power settings
simulate this circuit – Schematic created using CircuitLab
Figure 5. By using elements with power ratios of approximately 1:2:4 a multi-pole switch can be used to create a binary pattern to generate seven power settings (and off).