Heating Nichrome Wire with Arduino Uno

Perhaps if you explained WHY you want to do this?

The problem I was running into was my lack of experience with Pulse Width Modulation. I do not know how to control the light to warmly heat up, as you say, but if there were a way to do this without overly complicating the entire process, that would be great to know!

Perhaps if you forget PWM and just concentrate on turning a pin on and off based on a millisecond timer you could get it done.

on and off based on a millisecond timer

Is that not what I am trying to do currently? The problem it brings up is that the numbers are too high. 12 Volts and 5.535 Amps are something that I too would not want anywhere near my face

But if you only apply it for 1/4 second, how many watts is that?

Are you trying to prevent the goggles from misting up?

That is correct, but perhaps I have been thinking about it wrong.

Clearly. Doing some experiments and getting some experience would help clear that up.

I knew that 1 degrees Celsius is about 0.55 BTU

No.

Still 67W. but only 16J

It is still as many watts. 12V x 5.535A = 66.42W

There is a confusion between power and energy here.

Energy = 12V x 5.535A x 0.25s = 16.6J

Ha, you beat me to it there, John

Yes, and the Ampere ALWAYS has a time connected to it because it is a count of the electrons passing a point on a circuit in ONE second.

For "small" amounts of heating, you can use relatively high-value resistors.
For instance, a 100ohm resistor with 12V across it is about 1.4W (use a 2W resistor!), which should be much more manageable than a nichrome wire. Make that 10*10ohm 1/4W SMT resistors connected in series with fine wire or on a thin PCB, and it wouldn't even be that much bigger than a wire.

Or, consider lightbulbs operated at less than visible brightness (finally! An excuse for all those internally-illuminated space helmets you see in SF Films! (although the non-linearity of filament resistance may be problematic.)

I have been thinking about this idea, though midterms gutted me for the most part. What kind of lightbulb were you thinking that would be small enough to fit inside of goggles, or possibly just outside of them? I know about terrarium heaters, though those bulbs seem quite a bit too large.

They're called "Grain of wheat bulbs", typically sold in small quantities for adding lights to scale models (HO trains, for instance.)

5mm LED for scale:

The whole idea is a crackpot idea to begin with.