I have a Rheem Heat Pump and a White-Rogers Thermostat. Right now my heater will heat the room to the exact temperature I have it set to, but it never shuts off. It does not continue heating, so I can only assume the fan is what is still running outside. Any way to fix this

Unless you just installed or had the thermostat installed recently, I would not point at the thermostat as the problem. With what you have described I would suggest have your units serviced as it sounds like a loss of charge, or failed defrost control board. The "Aux" comes on when the unit is using secondary heating (electric heat strips). That occurs when the demand temperature (what you set it to) in Heat mode is more than the current room temperature, usually ~2-4 degrees higher. Also happens in defrost mode. Defrost is a heat pump cycle that melts any build up of ice on the condenser unit (outside unit). That process is simply the unit running in cool mode which will heat up the outside unit to melt any ice. Defrost cycles vary with manufacture but usually you can tell if is in defrost by looking at the outside unit, during defrost the unit will be warm or hot sometimes there is steam and the compressor will be running but not the fan. Defrost only happens on heat pumps in "Heat" mode. Rheem has a 10 yr compressor and parts warranty, so call the installer or Rheem authorized service company.

If you turn your heat on and the temperature is set 3 degrees above what the actual temperature of the room, the auxillary heat will automatically come on. The auxillary heat is an electric heat strip that provides heat to your home while the heat pump is in defrost cycle or if there are extremely low temperatures outside. Try not to set the temperature more than 2 degrees above the actual temperature of the room. Hope this helps.

if this is indeed a heat pump you rthermostat should also have a emergency heat setting does it work on that setting... a heat pump on heat wuns the outside unit and has a recersing valve that changes the refigerant flow ..is the outside runnignduring heat mode... if you turn the thermostat in emergency heat the outside should shut down and indoor heat should come on...of this is not happening you have a wiring issue if both are not working... braeburn thermostats usually have behind the cover dip switches... i am not exactly sure what model this is but if indeed a heat pump the thermostat should have a r,w2,y,e,g,c,o,and b terminal... rheem wiring should be as follows
red to r white to w2 , g=green , yellow to y terminal there should be a wire hooked to the b terminal usually brown sometimes orange on the b terminal that is your reversing valve terminal.
you are going to have to make sure the thermostat is configured to energize the b termianl and will have to go into the installer setup to do this...hopefully you still have the paper work on thermostat... most heat pumps use the o terminal for reversing valve but rheem uses the b terminal
hope this helps out some repost with anymore probs...also make sure the switches are set to electric or gas whatever you have heat pump or not etc. inside thermostat

You have a faulty thermostat. Very easy to replace. You can find a new thermostat at home depot.

follow this guide:
Diagnostic: Set SYSTEM Switch to HEAT and raise
the setpoint above room temperature. Within a few
seconds the thermostat should make a soft click
sound. This sound usually indicates the thermostat
is operating properly. If the thermostat does not
click, try the reset operation. If the thermostat does not click after being reset contact your heating and cooling service person or place of purchase for a replacement. If the thermostat clicks, contact the furnace manufacturer or a service person to verify the heating is operating correctly.

MANUAL OPERATION
• HOLD TEMPERATURE — With the SYSTEM switch set to
HEAT or COOL, momentarily press HOLD button. HOLD
will be displayed. Use UP or DOWN to adjust the temperature.
The thermostat will hold the room temperature at the
selected setting until you press RUN button to return to
program operation.
This is on page 6 of the manual
Link: Installation Instruction

No you need to change your t,stat. Go to home depot or Lowes and get one easy to install Any problems please get back to me I will walk you thru. Rus

Go to http://www.honeywell.com/ look up your therostst model No RTH7600D

Turn up your outside thermostat in the outside unit.
You should have about 3 degrees difference in one stage to the next. So I would change the thermosat with one that has three stages of heat.

You most likely have a heat pump, the aux heat (usually electric) comes on anytime the room temperature is 4 degrees below the thermostat setting. Does the buzz go off when the aux heat lite goes out? If the aux heat does not shut off then the primary heater (heat pump) is not putting out enough heat to satisfy the thermostat. I need a little more info. Do you have a heat pump? Is it working?