Last summer our water heater gave way and we replaced it with a "moe efficient" one. Well I now have a problem I never had before. The shower is closest to the hot water heater and works fine until someone turns on the water somewhere else in the house and then my shower gets ICY COLD. It's a rude awakening in the morning, every morning! It lasts a few seconds to 45 seconds and it's COLD. Any thoughts?? Thanks.

And you never had this issue with the old heater before it failed?

No, just after the new one was installed.

Was the installer using a torch to sweat the fittings to the tank? After the shocking cold water hits does it return to full on hot and stay hot?

Not sure about the installer question

After the cold water lasts for a little bit then it will go back to close to where I had it sometimes I do have to turn the cold down just a little like very little to get a little more hot.
It is just odd to me that I didn't have the issue prior to the old 25 year old water heater and now I have the new one with the issue. I thought maybe there was some type of water conservation item built into the new one.

Do you have a hot water recirculation line?

Is there a valve to the hot water heater that's partially closed restricting flow?

Flush the heater by attaching a garden hose to the drain spigot. Open the spigot but do not shut down the incoming supply line. Put a twel of nylon sock over the end of the hose to see what flushes out. Do this for about 5 minute and see if the hot water from the hose changes temp rapidly like your shower