Discipline the whining like any other wrong behavior. Modeling and setting examples is what you can do naturally in addition to that, but it won't stop the behavior. It will just allow your son to make the decision to quit whining one day whenever he wants because there is no serious reason to stop. YES he can become a big whiner, I know tons of whiny toddlers who grew into pouty whiny older kids. He needs your enforcement learning to control that urge so it can become natural to him to resolve himself. My 3 year old son took tons of discipline on the whining, he was a whiiiiiiiiner by nature, but he had it nipped by around 2 1/2. He'll still occasionally try it, but a warning suffices because he knows there will be consequences if he continues.
Don't give into the fact that he is "easy to upset" Most kids this age are! Some are taught to control it, some are allowed to melt down all the time. Your choice, but it takes being firm to see a happier more mature kid evolve. I thank my lucky stars every day for three non whiners.
Not ONLY should you not "give in" to the whining (OF COURSE), but he ALSO needs a firm consequence for it when you have given him a calm warning and the chance to stop, but he decides to continue. Don't fuel his self pitying fire by questioning him about his feelings when he's whining. Step one, warning to quit whining when there is obviously no injury or serious problem. Step two, consequence for continuing. Step three be sure he doesn't get what he was whining for until he earns it with good behavior and asking properly. Step five (optional) lecture him on whining (if you must) at a separate time, NOT during discipline. He's a male, and a toddler, He doesn't want to talk about feelings any more than a man does. Quick, concise, firm teaches the fastest and lets him learn to handle things on his own better without lots of "working through it and attention /sympathy" from you. Again, give him LOTS of cuddly love and nurturing of sadness at the LEGITIMATE times.
To clarify, this is NOT prohibiting FEELINGS in your child, this is allowing them more freedom of expression for real emotions by nipping the chronic habitual whining. My kids all have their full spectrum of emotions and they are allowed to feel mad and sad, and we do comfort and nurture them all the time. But they don't whine and throw fits. There's a difference.
Good tips on how: Back to Basics Discipline by Janet Campbell Matson.