Seriously, Heimerdinger is pretty broken 1v1, if you are really looking to dominate people. He has very few real counters in lane and will push and towerdive and zone/harass you forever... he will likely push your base down way before you can even get close to finishing most of your build. He can also build quite tanky and still do very close to the same damage/dps. His lane mechanics are broken, and even late game he is much stronger in fights anytime he can force you to fight where he wants you to, which in 1v1 is pretty much always.
Against a physical champ, rush Glacial Shroud and Sorc shoes and watch them cry as you regenerate what little damage they manage to do to you through your armor while nearly all of your constant damage (tons of mana AND a bunch of cdr in one item... shroud actually has very good stats for him and is very quick early cooldown reduction which is great for him with his high early base damages) and is IMPOSSIBLE for them to trade back. Your silencing grenades and heavily regenerating minions will hurt their last hitting badly. At that point you can safely build up ability power to eat them alive, adding more tanky items whenever necessary (Rylai's is still decent for him in 1v1, unless you built RoA instead).