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The power needed to power the laser, if identical, is what determines the temperature here, not the color.
A thousand watt laser is going to make the lead melt while a 5 watt laser won't.
Another limiting factor is how fast the lead/target material can dissipate the heat. A 10kg block of lead is going to stay a lot cooler than a 5 gram piece of lead.
The colour of the laser has no influence on the final temperature, at all.
The photons are just transferring energy from a to b. And whether they can do it fast or slow doesn't really matter. Both blue and red photons are subject to the law of conservation of energy. The amount of energy you put in is the amount of energy you get out.
In reality there is probably a difference in how efficient a blue and red laser diode are, so there are losses. And if one is slower than the other, the target material is losing energy to the surrounding air. And that's why you'll get different temperatures.
In an ideal setting with exactly identical lasers, where the only difference is the colour, the end result is also exactly the same.
You misspelled color
Both "color" and "colour" are valid spellings.
cooler
Im in the privileged position where I can say that I was educated to pronounce and write in British English. And while I'm not a native speaker, I'm confident that my knowledge of the English language surpasses most of native speakers in the US, if not 99%. My spell checker is biased for us English.
Now if you excuse me I have to go back to my flat, with my lorry having chips and candy floss in the boot. Do you even elevator bro?