Thanks for asking here at JustAnswer
Do you know if the replacement plumbing was the same size as the old plumbing. It could very well be that it was undersized. What material was used for the replacement?Would it be possible to take a photo of the water heater showing the plumbing coming out the top? I can help you with this, it may take a little time.
Ok, you need to send it to yourself and use the feature here in the text box to insert the picture, but if the piping wasn't replaced that eliminates that. Was a filter, softener or any other device installed with the remodel?
If your plumbing is galvanized, then yes there could be a problem with rust. But I am suspecting that the problem will relate to the tub valve itself. Is the tempature adjustable? Or have a stop limit on it?
Are they the same brand valve? The picture came through great by the way. Could you take a photo of the shower valve unless you know the brand name and model?
Send the pics.
Ok, we'll do this a little different.
Check out these sites and pick out your faucet, then get back with me.
I believe this is the Jado faucet?
First is an exploded view of your valve. Second is the installation instructions for setting the tempature of the stop on page 2. The American Standard should be very similar in design.
Ok, that was good info there. Does the tempature get hot enough? If so how long does the temp last before needing to turn it hotter?
Ok, use this diagram: http://www.jadousa.com/assets/repair/853401_repair.pdf
I believe you have some trash or debris in the cartridge on the hot side of the valve. Remove the cartridge and try to wash out the debris. Make sure the "screwdriver stop" is fully open when reinstalling the cartridge.
Behind the handle you adjust the tempature with. It will be #2 on the exploded view. It is called the "Pressure Balancing Unit". You need to feel comfortable in your ability before taking this apart, if not I would call a professional.