Installed small new hot water tank under kitchen sink and get lots of air from hot
Water and some from the cold. Never get really hot water and most of time water is
Just cold. Adjusted the temp settings and does no good. The mfg said there was air
In tank not allowing water to heat, so we bled it and does no good. Also had well
Repairman look at water system and bled it too. He said everything was fine even before
He bled it to make sure.

Any suggestions?

If you failed to bleed the tank before the element might be burned out and it sounds like that's just what's happened. It sure sounds like you've turned the power on,(have you checked the breaker?) Check the element before we worry about the air. If the tank was installed correctly and the tank bled and filled with water there should have been no air at all except what comes out I\of the hot water faucet on your sink.
Was this installed by a licensed plumber. Can you describe how it was hooked up? What's supplying The heater? Was the feed taken off the hot or cold lines? In short I need a lot more information then you've furnished. I want to know exactly how this Hot Water Tan k was hooked up and be sure to check for a burned out element. Regards, Tom

In additoion to Tom's response: there is really no way for air to enter your house plumbing system. Once you bleed the lines, all you should get is water. Do as Tom said: check elements then breakers. Don't plug it in unless the heater is full of water and completely bled. Back to you. Milo