Now we're in a heat wave (90+ with very little rain for past few weeks) and the sod is starting to die. If I had to guess, the new sod is roughly 50% green with the rest seemingly dead. It is very easy to tell where the old grass ended and the sod was planted, as there is a pretty distinct line where the 90% green ends and the 50% green begins.

I've been mowing on the 2nd highest setting every 10 days or so. I am going to move to the highest setting and mow less frequently. I've been mulching the clippings, should I stop this?

I've also been trying to water the grass every few days in the mornings. Any idea what may be going on? Losing the sod would be a real bummer!

What did you amend the soil with? Was it compost or peat moss? How much? Either compost or peat can act like a nitrogen sink in the soil. If they are fully decomposed, then all the nitrogen in the soil will temporarily go toward decomposing the buried twigs, leaves, and sticks from the buried organic material. Sometimes it takes a year or more for the turf to really come back after burying too much of the wrong kind of organic material. Compost and peat should be applied to the surface where they can decompose from the nitrogen in the air.

Did you roll the sod down. The most important step in sodding is to ensure you have good sod-to-soil contact. A water fillable roller works very well. You cannot just put the sod out, though.

When you first laid the sod, did you water it for three weeks, every day, 3x per day, for 10 minutes? That is necessary to establish the root system down into the underlying soil. New sod is just like new seed in watering requirements.

Mulch mowing is not a problem. It's a good thing. Some people mulch mow from 6 inches down to 2 inches. In that case they should get rid of the clippings to avoid fungal disease and smothering the lawn. But you are mowing correctly, so keep it up.