Well, since we now want healing for teams, I guess I could do that.
The most healing that can be done to a team consistantly, is 4 HP, with Fanatic playing Embolden on Tempest. Then Tempest using 2 copies of Cleansing Downpour.
The most I could think of, that is currently possible to regain any given hero target in a single turn is 15 HP. It requires Tempest, Scholar, Argent Adept, Omnitron-X, and the fifth hero target to be the focus of the healing. Tempest would need both copies of Cleansing Downpour in play. Argent Adept will need the Lyra, Harp, Pipes, Horn, Drum, 2 Rhapsody of Vigors, Alacritous Subdominant, Inspiring Supertonic, and Inventive Preperation in play and a Vernal Sonata being the third card on the top of his deck.. Scholar will need both copies of Proverbs and Axioms, one on top of his deck and the other in hand, with a copy of Don't Dismiss Anything also in hand. Omnitron-X will needs both copies of Inventive Preperation in play.
On Omnitron-X's turn, at the start he will heal the fifth hero for a total of 2 HP. Then on Omni-X's power phase, he will Timeshift the Scholar, putting Proverbs and Axioms into play, causing the fifth hero to regain another 2 HP. Then Tempest will take the damage to use a power, Cleansing Downpour, the fifth hero regains another 2 HP. Argent Adept will also use a power, He will activate the Harp for the perform of Inspiring Supertonic, into the Lyra for Inspiring Supertonic's perform, which will finally activate the Pipes, for both copies of Rhapsody of Vigor, healing the fifth hero for yet another 2 HP. Then we will back track to the Lyra's accompany, which will be Inventive Preperation, allowing Scholar to play another card, which so happens to be Proverbs and Axioms, regaining the fifth hero another 2 HP and allowing Tempest to use his second copy of cleansing downpour again, for another 2 HP. Then we finally get back to Argent's string of powers, the Harp's accompany will trigger Alacritous Subdominant, so Argent can use a power now, he'll use that to activate the Horn, which will then do the perform of Rhapsody of Vigor to heal the fifth HP be 1 HP. The accompany will the the Alacritous Subdominant again, so another power which will be the Drums. Activating the perform of Rhapsody yet again, for 1 HP. He can now also activate the accompany of Inventive Preperation again, allowing Scholar to play Don't Dismiss Anything, which will play Vernal Sonata for an additional 1 HP.
Now if you want to factor in the environment, currently only Ruins of Atlantis and Realm of Discord can effect healing on the hero's turns. In the Ruins case, if both Phosphorescent Chambers are in play, increase every instance of healing by 2. That is 11 Instances, so an additional 22 HP, making the total 36 HP recovered. Kind of impossible at the moment.
In the realm, if the fifth hero is always going to be effected by the Positive Energy Field, that will be another HP for every card that entered play, that's another 7 HP, so that's 22 HP total for that.
Edit: have actually came up with a slightly better one, instead of Omni-X, have Greatest Legacy. This will move the turn in question to Scholar's, where he'll just play the Proverbs and Axioms instead. Greatest Legacy will need Motivational Charge in play and Inspiring Presence to be the third card on top of his deck. For Greatest Legacy's two power uses from both Proverbs and Axioms, it will be to Gung-Ho the fifth target for 1 HP, then Motivational Charge for another 1 HP to the fifth target. Finally Don't Dismiss Anything will play the top card, which is Insiring Presence for another 1 HP. Bringing the total to 16, rather than just 15.
Edit2: Had forgotten, Argent Adept didn't use any powers from the second Proverbs and Axioms, so he could use Vocalize to activate Rhapsody of Vigor again, bringing the total to 17 now.