Remember that he doesn't counter all mid laners. Here's a few champions that I've used against him, they work really well.
: You can usually kill all 3 of his turrets with one Mantra Q, she's probably his biggest counter simply due to the fact that she can quickly shutdown all of his turrets before engaging with her Snare + more Q spamming. Also, her shield can block most of the damage his poke does.
: Everything she has is AoE except her Machine Gun, I mean, "fangs". Try using your Smoke Grenades, I mean, poison, on his turrets and go Rambo on him after they're down. Also I haven't experimented, but I wonder if her ultimate effects his turrets? She's pretty hard for Heimer to fight since she can very quickly disable his turrets and blow up Heimer.
: What I do is simply all-in him post-6. I don't poke the turrets down however, I simply just dodge his Stun Grenade and all in him. After I get really low, I simply ult and clean him up. Usually with her ult + heal/movement speed, you can ignore pretty much his entire combo rotation and most of his turret damage. And since her E has AoE, while you're hitting Heimer in the face with a Ranged Sword it also does splash damage on the turrets.
: Soldiers > Turrets. He can all-in Heimer post-6 and is just a lot stronger. On top of that, his scaling is colossally better in comparison.
: I've never seen Syndra do that poorly against Heimer, or at least while I played her. Her Q counters his turrets, she has a better and more reliable stun/knockback thingy nobody can figure out how to use, and she can just instakill him post-6. I believe you can throw his turrets back and also throw them at him too? I don't remember, I haven't played her in months.