What role, if any?

Motivation. If I feel strongly, I will defend/advocate strongly. If I'm motivated, I will research the topic at hand so I can present my arguments rationally.

your point about emotions being an interference of rationality i accept. but I do not believe they can be eradicated from it if comes from people. Watson perhaps. besides that would take all the fun out of it.

Emotions, just to name a few (Amazed Foolish Overwhelmed
Angry Frustrated Peaceful
Annoyed Furious Proud
Anxious Grieving Relieved
Ashamed Happy Resentful, [therapistaid.com] )

These emotions are mostly either considered good or bad(evil). They are relative or subjective as to the person experiencing or displaying them.

I make this speculation: For those people that display higher levels of emotion during discourse, this high level of emotion display requires more energy and perhaps brain activity which then would possibly effect thinking about the topic. The ideal, thoughts of words the person is trying to process out into speach while in a highly emotional state might be like having a lot of apps. running at once on a slow computer.

Defination: Rational - based on or in accordance with reason or logic.

Logic is about good and evil. Something logical is said to be of "good" reasoning. And, illogical, something with fallacy, the opposite of good which would to be an evil.

You say, "Since emotions are by and large out of our control, ..." I would not say that is exactly correct. What is not "controlled " is the variable degrees of emotions that each specific person might display during rational discourse. One person may show more happy or anger about a topic that another person might display.

Rational is very much strongly connect with emotions which the display of the amount of emotion from one person to the next can vary.

We cannot be emotionless but we are capable of rational debate...

Strong emotions can kill discourse or any thinking endeavor. Emotions are often rooted in thoughts. The destructive kind of emotions well up because of untrue negative thoughts.

Yet emotions exist for a purpose. I see it like salt. You can’t live without a little salt, but a lot of salt will kill you.

Beyond thought we have pure awareness. Communion with whatever it is that is the basis of reality might give us insight and keep us on course. The only emotions involved are serenity, hope, love, appreciation, ecstasy, etc.

that's what calculators are for.

Rationality, while useful, is not enough.

the reason to have the discourse in the first place. curiosity, the desire to know etc.? the passion to find love, to save a life, to have a sense of urgency?

In which case the only course of action to follow is Bentham’s utilitarianism - the greatest good for the many.

That has never caused problems in the real world has it!

Great theory, crap practice.

Keen observation, I concur. No place for emotions in serious conversations on what could be considered touchy subjects.