Can eating disorder and recently fever and sore throat cause a slight increase of heart rate to a 4 year old boy?

Eating disorders, : anorexia & bulimia, are rare in 4-year-old boys. If his height, weight & head circumference are not following their %iles on growth curves or he has pediatric undernutrition, weight-for-length < 5th % ile, he needs an evaluation for a medical cause. If okay, see healthychildren.org for healthy diet at 4 years. Fever can increase heart rate. Fever + sore throat require a throat culture for "strep"

Yes: Fever causes a predictable increase in baseline rate by 10 bpm/degree Fahrenheit. Illness of any sort can trigger stress hormones that do the same. Sounds like the kid needs to be examined/treated.