Yes, use a thermometer to insure that cooking temperatures meet food safety guidelines. Hot food should be hot, above 150 degrees F. Cold foods should be cold, below 40 degrees. The main reason for having Dutch oven cookoffs, after all, is to pass along the art of Dutch oven cooking. Reward good efforts at interaction with the spectators. Watch how the team members interact with the judges, and compare that to how they interact with the spectators.
Cleanliness is a major factor during the field judging portion of the cookoff.
Utensils, ovens, ingredients, prep areas, and personal cleanliness should be watched. Reward the use of wash areas, table coverings, washing of hands, and covering food items from contamination. This may be outdoor cooking, but cleanliness is still very important. Penalize the lack of cleanliness in preparation and cooking areas, ovens, ingredients, and hand washing. Dutch oven techniques showing proper use of ovens, heat source, tools, and utensils should be judged.