I'm sure this was asked on Photrio before, what does warm paper developer do to photographic paper.
A "weak" developer (or a regular developer nearing exhaustion) is unable to fully reduce the silver halide in the emulsion, shifting it to warm tone. A warm paper contains halides that are more difficult to reduce, and a warm tone developer is weak enough make it more difficult to totally reduce the silver halide. Cold vs Warm is about chemical reduction (contrary to oxydation):
> Totally reduced is cold tone
> Not well reduced is warm
> Something in the middle is neutral
If you add bromide then reduction is lower because the chemical equilibrium tends to reduce less, and you get a warmer result.
Just consider that the severity of the chemical reduction depends on if the halides in the paper are more/less dificult to reduce, and on the developer's capability to reduce more/less, adding bromide you reduce less.
Some developers like Ansco 120 (Glycin) are suitable to modify tone a bit by adjusting chemical exhaustion, the more exhausted the warmer, fresh and used developer can be mixed to adjust warmth. With other developers it is more difficult to adjust exhaustion in an stable way, but you also adjust tone in a way or other. IMO a sound work may end with some selenium or the like, you do the job there.
The degree of development depends on time and on temperature, one thing can be traded by the other. Not developing to completion may slightly change a bit the warm/cold tone and contrast. ...but as Ralph pointed things are not always linear and some extended time may allow some additional crystals to develop increasing contrast.
I my targeted pale gray was now way lighter. It looks like for me to work with the analyzer, I have to keep the paper developer around 70°.
Let me mention another potential factor weakening the highlights
Also exposure time on paper has an impact.
Let's imagine we have a correct exposure at 20s. Then we decide close diafragm by 2 additional stops. Well, our new time will be 80 seconds, isn't it ? This exposure will be mostly correct for the shadows (in the scene) than throw a lot of light on paper, but our highlights (scene) ara very dense in the negative and of "low intensity": We may have Low Intensity Reciprocity Failure specially in our highlights, delivering a lighter grey, and increasing the perceived contrast.
This not only happens when stopping more the lens... if you rise the enlarger's head to print to the double size you have x4 the area so time has to be compensated by an x4 factor longer, again that corrected exposure will be not perfect for the highlights receiving low intensity and also at risk of having LIRF. For this reason when crafting an smaller prototype to later make a big print the lens may be stoped to deliver the same illumination than when making the big print, for example, if we are to make the big print at f/5.6 then a prototype thar has half the size should be made at f/11, in that way the big print will receive the same light intensity than the smal print, we won't require a time correction, and the highlights will be equal than in the prototype.
So, like with film, reciprocity failure is well higher in the areas receiving a lower intensity... An equivalent but longer exposure relatively weakens more the (scene) highlights.