There doesn't have to be a fever for there to be a "bug" going around. It can be kind of low-grade which is why he's acting okay. It doesn't sound like any kind of food poisoning because he's not constantly throwing up - just after he eats, right?
Not sure what he's eating. Start with the tried & true ginger ale - stir it so it's flat - the ginger is a real stomach-soother. Wait an hour. If it stays down, try some more. Wait an hour. Then start SLOWLY with the "brat" diet - bananas, rice applesauce, toast. You can try a little jelly on the toast. When they don't eat, their sugar level drops and that can cause more throwing up. Just try ONE food, and always wait an hour. Some people try Pedialyte to get the same result as the ginger ale. I would absolutely not give him any dairy or any meat - those things are tougher to digest and can irritate an upset tummy.
If there is no pain in the stomach/abdomen (try gently pressing) and he continues to act fine, then there probably is no emergency.
Sometimes a stomach thing can move south into the intestines, so watch for diarrhea. For that reason, I would not give him fruit for a day. Stay with the bland stuff. No matter what he says he wants, stick with the "brat" stuff!
If it continues for another day, definitely call the doctor.
Good luck.