I'll guide you to the general area. There are a couple of ways to get there, but try this:
When you start the mine mini-game, choose the grey door on the upper left. Continue north thru a door. Then take the door on the right. Then take the door on the left. If you continue on this path, you'll get to an area with a glowing red outline.
The heart's room is directly connected to that red area. You'll know you've found the right room if you find a chamber with grey mine floor and an item in the center in something that resembles a mine-cart.