I recently had a water oak with heart rot cut down. The middle of the tree is a mushy consistency created by the fungus that caused the tree to rot as far as I know. We have an entire wheelbarrow of this material left over and I'm wondering if it could be used in my compost pile or if it could be mixed into the soil by itself.

Thanks in advanace.

I am not an expert on heart rot, but I would think it would actually help your compost pile. It only feasts on decayed wood, so I don't think it would harm anything healthy. And it would probably help speed up your compost pile. Fungi is very important to the compost pile.
Having said that though, you can always shoot an e-mail to your county extension office to be sure - they usually answer back promptly.

Plants growing in rotten wood is basically the concept of a nurse log. The wheelbarrow looks awesome. I bet you could put it directly in the garden. (or maybe not, it's a bit hard to tell texture from an image)