Heimerdinger has always been a reasonable pick down mid lane, stomping anyone who doesn't know how to play against him. Up in the melee-dominated top lane, however, there are fewer counters to Heimerdinger, and in my opinion that's where he shines. Let's go.

Pros

Incredible harass against melee top-laners.
Powerful all-in at level 6 with ERW.
Highest base health regeneration stat in the game so building health regen on him is efficient.
One of few champions able to turn a gank into a double kill.

Cons

A big target for ganks.
No mobility.
Can fall off late game.
Deprives your team of a tanky top laner, forcing a tanky jungler/support instead.

Generally you want to place turrets in an arc shape, with the middle one behind where your melee minions will be. Use them to pick up farm that you miss early game, and as a harassing tool when someone pushes too far. If you autoattack an enemy champion, it marks them and your turret prioritizes them for the next few seconds, as long as they stay in range. Ideally place your first turret furthest forwards so that if you replace it while kiting back during a gank the turrets closest to your tower remain standing and the furthest away one is replaced.

Try to keep the bush by the river warded as you're almost always pushed forwards, and if you overextend too far it's easy to be ganked. Of course, when you're up to their turret, that's the most vulnerable time. Heimer boasts the highest health regeneration in the game, but otherwise you're still squishy early-game. Even if you don't die to a gank, it's easy enough to lose one or both of your summoners.

Mid game is where this build shines.

Split push where you can, and aim to take objectives (Dragon is straightforward and Rift Herald is a big benefit early on. Take their top tower asap).
In terms of teamfights I'm usually there to try and delete the carry with stun + RW, or to break up their team with RQ. Bbuilding Zz'Rot Portal on Heimer helps you further to splitpush. The defensive stats are nice and the active helps to split their team up to force fights in your advantage, or even to allow your team to sneak Baron.

Banner is good in mid-lane for creating roaming opportunities, as well as for helping you to catch up from a CS deficit. It lets you push lane with the active, so while your opponent is shoved under tower you can take an objective or a kill and tower in a sidelane. The 60 AP is nice, and the MR aura helps when your team inevitably groups up. The CDR also helps you to hit 45% with Zhonya's, Abyssal Scepter/Ionian Boots and 10% in runes.

Heimerdinger's ult empowers his next ability. His ult-Q (Turret) becomes bigger, outputs a lot more damage with a small slow, and its beam recharges quicker, but it lasts a maximum of eight seconds. His ult-W (rockets) fires out four waves instead of one, with 45% AP on the first rocket that hits a target, and 9% on each other that hit the same target. His ult-E (bomb) bounces twice after its original landing, packing an 80% slow on anyone in range and a stun on anyone it hits directly - but it only deals damage once.

If you're being ganked, and you have a feeling you can turn it into a double kill (ie mini-turrets down and the lane opponent is low) opt for ult-Q. It provides high dps with the little towers, and combined with the stun on E and the damage from W, you can output a lot of damage. It's also a very safe choice in teamfights against tankier comps.

If you want to push for a level 6 all-in, ult-W without a doubt. Position yourself so there are no minions between you and them, stun them with your E, then ult your rockets. If you hit them with every rocket, it's 500 magic damage plus 216% AP ratio at level 6. In teamfights, if there's someone in particular you want to focus on, ult-W gives the best damage output, especially in the mid-late game where if you catch their ADC out of position in a teamfight you can get serious damage on them with ERW.

Ult-E... is a little underwhelming. It's useful if you're chasing someone with the rest of your team to let them close the gap with its huge range. However, ult-E is a good engage if your team has no real frontline, with an AOE stun/heavy slow strong enough to let your team engage.

Heimerdinger is a solid pick down mid-lane, and he has been for a while, but as you can see there are plenty of arguments for why he thrives in the top lane. Dominated by melee champions, top lane gives him an environment where he can harass from a safe distance, push lane while surviving ganks, and deny plenty of CS.