Temperature is a scalar value measured in some way similar to degrees Fahrenheit, or degrees Celsius. Fuel is some scalar quantity describing the density of the unburnt fuel in an area. Fire is the weirdest one, and is a scalar quantity describing the power of the fire at the particle. For a simple glowing fire effect, you can multiply the Fire channel times a Orange vector input, and output that into the Emission channel of Krakatoa. That will make the particle self-illuminated in a manner proportional to the amount of fire at the sample point.
A prettier example would use the temperature at the location to affect the color of the fire, similar to black body radiation (en.wikipedia.org/wiki/Black_body).
I’ll post an example of what I would use in a few days once the release is finalized.