Below is from the Rheem Fury use and care/install manual. It says don't put on a blanket, but if local code requires you to use a blanket, don't put it on top.
Insulation blankets, available to the
general public, for external use on gas
water heaters are not necessary. The
purpose of an insulation blanket is to
reduce the standby heat loss encountered
with storage tank heaters. This water
heater meets or exceeds the
Appliance Energy Conservation Act
standards with respect to insulation and
standby loss requirements making an
insulation blanket unnecessary.
The manufacturer’s warranty does not
cover any damage or defect caused by
installation, attachment or use of
any type of energy saving or other
unapproved devices (other than those
authorized by the manufacturer) into, onto
or in conjunction with the water heater.
The use of unauthorized energy saving
devices may shorten the life of the water
heater and may endanger life and property.
The manufacturer disclaims any
responsibility for such loss or injury
resulting from the use of such
CAUTION: If local codes require the
application of an external insulation
blanket to this water heater, pay careful
attention to the following so as not to
restrict the proper function and
operation of the water heater:
Do not cover the operating or warning
labels attached to the water heater or
attempt to relocate them on the exterior
of insulation blanket.
Do not apply insulation to the top of the
water heater. This will interfere with the
safe operation of the draft hood.
Do not cover the burner access door,
jacket door, gas control (thermost at)/gas
valve or pressure and temperature relief
Do not apply insulation to the bottom of
the water heater or the area where the
combustion air inlet openings are
located. This area must be unobstructed
so as not to restrict combustion air flow
to the burner.
Inspect the insulation blanket frequently
making certain it has not sagged and is
restricting the air flow to the combustion
air inlet openings (perforation holes)
located around the lower perimeter of
the water heater jacket. This could result
in an unsafe operating condition