I've been struggling with this one for a while now. The two options I see are a high AP/tanky build involving tear and a rod of ages to make use of the bonus mana and kiting around turrets but this is often a long-term strategy and ARAM's often end sooner than that. How ever with Heimer's excellent poke, going for the chalice upgrade plus another cooldown reduction item can mean tons of turrets, rockets, and stun grenades. This goes the same for offensive AP talents verses some in support for faster cooldown in early and late game.
What's your heimer strategy in ARAM?