People skills guru, Robert Bolton believes that the rational approach to problem solving rarely works 
when emotions are strongly engaged as emotional arousal makes us act differently than when we are in moments of calmness.
In fact in an emotional state we appear to be more equipped for a brawl then we are to problem solve.

Bolton's theory is backed up by physiological research, which suggests that when we are angry or fearful our adrenaline flows faster and our body strength increases by 20%. At the same time the liver pumps more sugar into the blood stream and the rest of the body demands more oxygen from the heart and lungs. This causes the blood supply to rush to the major extremities of the body reducing the flow to the problem solving part of the brain. So, when feelings are strong often it is a sound strategy to deal with the emotional aspects of conflict first as  we are physically unable to be rational and to effectively manage conflict at that point in time. So then how do you effectively handle the emotional side of conflict and deal with the issue?
Here are some tips to help you deal with the issue of emotion and conflict:

Consider if you are prepared for the conflict

Simultaneously dealing with conflict and emotion must work in two ways. Not only do you have to deal with the emotions of the other person but you also need to personally have enough emotional energy to deal with the conflict itself . Often conflicts arise at times or places that are not appropriate or convenient for both parties. One of the ways to deal with emotion in this instance is to prepare for handling the encounter by making sure that the time to resolve the situation is right for both parties. This may involve finding neutral territory and scheduling sufficient time to deal with the conflict. The advantage of scheduling a later time is that it provides an opportunity to calm down and to problem solve more rationally.

Treat the other person with respect

Sometimes it can be difficult for people to properly communicate their feelings. Therefore it is very important that when people are emotional you respect the feelings that they are attempting to express and communicate. B y focussing on your body language, voice tone, facial expressions and by listening to them you are able to show respect for their position. Treating people with respect can quickly diffuse an emotional situation especially when you reassure them that they are valuable part of the group and allow them to express their point of view without interruption or criticism.

Focus on the problem and not the person

When emotional people can say things in the heat of the moment that they later regret. This doesn't mean that their feelings were not justified but in a moment of calmness they may have communicated how they felt in a more appropriate or functional way. It can be extremely difficult to de-personalise a problem especially if you are feeling hurt or angry. In order to focus on the problem and not personal issues, you might like to think about analysing the problem by focusing on questions that ask Why, How and What. Following the Collaborative Problem solving approach [pdf] can also be a helpful way of focussing on the issues and can help to take the conflict away from the personal issues.

Search Jointly for Solutions

Brainstorming allows a broader range of solutions or ideas to be put on the table. The most important part of brain storming or joint problem solving is that the parties involved in the conflict are allowed to express their opinion. Often it is not the solution that diffuses the emotion it is the process adopted that helps to diffuse emotion and resolve conflict. Following the Collaborative Problem solving approach [pdf] can also help when searching jointly for solutions.

Understand the other persons point of view

It is impossible to find a joint solution if you do not understand the other person's point of view.
This will involve listening and restating the ideas and feelings of the other person until you truly understand what they are feeling. This technique may be difficult and uncomfortable for some but restating what has been said is often the only way of knowing if you “got it'. This technique will take some practice, patience and perseverance until it becomes natural to you both.

Briefly express your own ideas and opinions

When emotions run high often the best way of getting your message across is through brief and direct communication. If you do not have an opinion it is always best to let the other person know this rather than sit in silence as this may frustrate the situation more. Often simply acknowledging the anger or feelings of the other person can diffuse an emotional situation and help to resolve conflict, however this must always be done sincerely.

Be Honest & Genuine

Being honest about the way that you feel and expressing your opinion is an important way of letting the other person know that you respect them and the relationship. If you are not honest or do not express your feelings you may in fact be doing more damage to the relationship and increasing conflict.

References:

Robert Bolton “People Skills” Simon and Schuster, Australia, 1986.