Yes, Heart of the Storm works with wands
In addition, whenever you start casting a spell of 1st level or higher that deals lightning or thunder damage, stormy magic erupts from you.
All the feature requires is that you start casting a spell that meets the requirements. And using a wand is still casting a spell, just with the aid of an item.
Specifically the Wand of Lightning Bolts says:
While holding it, you can use an action to expend 1 or more of its charges to cast the lightning bolt spell (save DC 15) from it.
Casting a spell is casting a spell. So it counts.
And the spell meets the other requirements as well since it deals lightning damage and is of the appropriate level.
Some magic items allow the user to cast a spell from the item, often by expending charges from it. The spell is cast at the lowest possible spell and caster level...
Since lightning bolt is a 3rd level spell, that is what it is cast as, which meets the 1st level or higher requirement.
The fact that the spell is being cast with a wand and uses a charge has no effect on the ability for it to work here.