Just as a quick text break down it's less about how much heat you're generating directly and more about how much heat is generated by a lack of ablation of the material. The more laser light is absorbed the cooler the actual substrate will be, because that energy is going into the ablation process rather than heating the metal itself. Less ablation = more heat. Like all things in life there are exceptions to that but generally this is the way to think about this process. Again, these are all blanket statements and there are lots of exceptions and weird edge cases BUT, here's a vague idea:

Lower speed means the laser is in any given spot for a longer amount of time. This typically generates more heat. Easiest to think about without getting a headache.

Higher power generally means more heat but only if ablation IS NOT occurring, if you're ablating, temps will still go up but at a much slower rate than if ablation was not occurring.

Larger pulse widths function much like power does in that higher pulse widths will generate more heat but also raise the chance of ablation. Lower pulse widths are commonly used when color hunting because they allow the gradual increase in temperature over longer periods of heating time with LOWER risk of ablation over all.

Frequency is the most obnoxious one due to it's function represented as kind of a bell curve shape. Very low frequencies don't offer enough consistency to heat or ablate metals. As the frequency rises so does the power output due to the laser firing more frequently, this of course raises the chance of ablation. To a point. At some point you will reach your peak power output frequency, where you will no longer see power returns for increasing the frequency. This is key for your use case as beyond this value you will start to see a dramatic downward slope in chance to ablate while retaining your max power output. Where you stop after your peak pulse power output will largely affect the oxidization effect you experience on the final mark. Contrary to popular believe that pulse width offers the finest control over resulting colors I generally find it's frequency that provides the granular adjustment. Confused yet?

At the end of the day speed and power will be set to whatever they have to be to get the reaction - beyond that frequency will be your best tool for adjusting the resulting effect while pulse width will be your best tool for enabling heating without ablation. A nice low pulse width will open more frequencies up to you than someone without MOPA functionalities.