Warmogs Heart at bare minimum 3000 hp
Just played game of aram as vel koz and managed to get exactly 2200 hp so figured id build warmogs for the heck of it... I had 3000 hp exactly and warmogs heart passive was not given. I waited the full 8 seconds outside of combat to regen health and got nothing. To quote the wiki "Grants WARMOG'S HEART if you have at least 3000 maximum health"