Never compare the best exotic armor piece in the game with that peasant of a chest piece.

The heart of the Praxic fire doesnt give you the extra grenade, you are talking about the Starfire Protocol chest piece. It gives you the extra fusion grenade. It doesnt stack with the gift of the sun perk on warlock. You can have 2 fusion grenades from the armour perk and use some other perk on that warlock skill tree.. You will not have 3 grenades

First off: You're thinking of Starfire Protocol. Second: No. No it does not.

I'm gonna go balls deep and assume that you mean Starfire Protocol. No you can't carry three grenades. It's basically there to allow you to use the other perks and have two grenades.