The last item is actually the Frozen Heart. I added Rod of Ages cause I think it could be a nice option instead of another item from the build, like Morello's or Abyssal... Depends on the game.

One big issue I have with the first item build is the RoA as the last item. What is the point of that?

Actually I'm still working on the build. I've tried it sometimes and it seems that it's kind of hard to deal with mana in the early/mid game, unless you get Clarity or blue buffs frequently. After putting 3 points in Strenght of Spirit, which would help Heimer's survivability, I was left with those two points. I wasn't sure about where to put them, but +7 AP at level 18 is not so bad.. However, I do understand that they could be better used somewhere else. I'm still studying this build.

Anyway thanks for the comment.

My objective with this build is give a little different approach to Heimerdinger. I'm trying to go a little farther from the usual Only-AP or Offtank builds, trying to make him an able-to-survive supporter in lane and in team fights, with small cooldowns, some good amount of AP and passives from his items (Rilays would make his missiles slow down the enemies, which is helpful due to their range, and the Abyssal+FrozenHeart would slow and weak everyone around him).