Since I installed a hot water heater 10 years ago I had occasional
problems getting hot water for a bath. It would come out hot for the
first few gallons, then slowly gets cooler until it is so cool I
needed to turn it off to keep the water I have, comfortably warm. Only
the first couple minutes was it fully heated.

I discovered if I turned on the hot water for a couple of minutes,
about a half hour before I take a bath, there will be enough for a
full tub.

A few months ago I had a energy efficient furnace installed and that
took the furnace's exhaust off the house's smoke stack, leaving only
the hot water heater to use the stack. -- that made the bath situation
even worse. It is luke warm from the start and gets cooler from
there.

I had our utility, whom we have a service plan, come out to check it
out. They couldn't find a problem, but decided to replace the
thermostat just to see if that helps -- it didn't. They finally said,
perhaps the heater needs to be moved so the ductwork will be
lengthened, since the hot water heater is now isolated on the stack.
They thought the heat might be being sucked out because of the short
distance from the heater to straight out the chimney.

Does this make sense? Should I really move the heater?