I have a question on how many amps a 16 AWG, 22 AWG, and a 28 AWG wire can handle. I know there are a lot of tables that give the max amps at room temp but I need to know how to derate this to 70 degrees C and have not been able to find any info on how to do this. Please help

 

The first thing you need to know is the insulation composition. The NEC handbook can help you from there.

 

Fuzzy:

Think of a wire as a resistor with a very low impedance value.
All wires have resistance to conductivity, and they're usually graded as ohms/foot (or ohms/m in the metric system)
That value will tell you how much power will be lost due to heat.
So an AWG 14 wire can only be so long when powering a 1hp motor before it melts, with wires usually rated at 70° C.
There are industrial wires rated at higher temperatures (more expensive, and less efficient), look for the wire's particular specs for that matter.

So the proper maximum wire length of any gauge to use on a project depends on how many amps at how many volts (translation = watts) your project will need to function properly. You can actually test this in real-life just by feeling with your bare hands how much heat is produced in the cable cord commonly used in electric heaters.
As a rule, fabricators of these items (read chinese) are usually greedy when it comes to spcifying the cord's appropriate gage.

 

Per NEC table 310-16, conductors w/ insulation rated for maximum 75C would be derated to 0.33, and those rated for maximum 90C would be derated to 0.58 - those rated to maximum 60C could not, of course, be used.