Most Heimerdinger guides and players will tell you to take Aery/Comet and rush Luden's for poke and just play a boring poke game that just overall feels weak. Basically the point of this is to burst down your enemy instead of just poking them. Doing damage means nothing if the kill doesn't go through, that's why i feel that comet is weak.

around 4:30 you should have enough to get blue pages (lost chapter), back immediately and depending on the position of the wave teleport(if the minions are pushed up just walk) then just use turrets as normal and use rockets sparingly to secure farm and poke every now and then. The real fun begins when you get a needlessly large rod and deal unholy damage. Start being a little more aggressive and PLAY AROUND YOUR TURRETS, try to predict the enemy's movement and get ready to smash your keyboard. The burst damage will one shot just about anyone.

I have a bad habit of getting into difficult fights and not warding, 3v1s and what not. With this build you can surprise the enemy with crazy burst from the insane early ap that nobody expects. Even if they rush magic resist you will still do way too much damage for them to all in you without severe punishment. Another one of my favorite things is you become like yasuo, you may go 0/10 but at 25 min if you farm well you can still solo baron and 2v1, you can turn it around late game, and most importantly you can carry.