He's old enough, and it sounds like he's verbal enough, that I think you could sit down with him and talk to him and tell him that his behavior is completely out of line and unacceptable. Tell him that you realize that he's probably in the habit of acting like this, and you know that habits are hard to break, so you will help him.
Then, seriously, bribe him. Tell him that he can fill up a jar with marbles, or a chart with stickers, or earn popsicle sticks, or whatever, for having a whole morning and a whole afternoon without tantrums. At first, make it short spurts of time. Morning = arrival to nap, afternoon = nap to pick up, and if there are no tantrums for the morning he gets a marble and none for the afternoon he gets a marble. Make his first reward pretty easy to get...like, ten of whatever you're using and he gets a lollipop (that would be a week with no tantrums). If he starts into a tantrum, at first give him a warning..."You're going to lose a stick if you don't stop before I count to three..." and partner this with TALKING to him about his feelings (frustration, disappointment, anger, etc) and some appropriate strategies for dealing with them.
Then after that first reward, re-evaluate...did he earn it pretty fast? Did he needs lots of warnings? Did it take him several weeks to earn it?
Empty the jar and repeat...after a couple times and he's getting the hang of it, change the game. Tell him "Hey! You're doing such a great job! Now to earn a marble you have to be pleasant all day! BUT...if you fill up the chart, you'll get [a slightly cooler lollipop, a popsicle, etc].
Eventually you take away the warnings, and at some point you start making him remember the stickers and the rewards...and somewhere along the line...he should get good behavior.
