The temperature alarm is beeping and the fridge and freezer continue to get warmer.

1. Check to see if the fridge and the freezer are overfilled Over-stuffing in the freezer or the fridge or both of these compartments will prevent the doors from closing properly and which can cause the fridge's to set off the beeping alarm.
2. Check the fridge door seals: Broken or damaged door seals may stop the fridge from closing all the way. This can also happen if the seals are dirty. Wipe clean the door seals with a soft cloth and warm and use soapy water and close the fridge doors. If the door still appears ajar then you have to replace the door seals.It is also quite possible that the inbuilt door-alarm which sets off if the fridge door is ajar for more than a few minutes has gone bad . This would need to be looked at by a qualified repair person . Until, you can call a repair person transfer all the food items to another cool place.
3. Check the fridge balance: To work correctly the fridge must be placed on a levelled surface. Even a slight tilt in the fridge structure can set off the beeping alarm. Check to see if the fridge is balanced evenly.
4. Check to see if the fridge exterior is warmer than usual: Check if there is adequate distance between the fridge and walls to allow for proper ventilation. If you have already ensured this and the fridge exterior still appears warmer than usual, have an appliance engineer to take look at the problem. If the beeping continues, switch-off the fridge.
5. Check the freezer: If your fridge does not have an auto-defrost function then excessive ice-build up in the freezer can cause the beeping alarm to go off . If you see a lot of ice build-up in the icebox or freezer, switch off the fridge and let the ice thaw. Once the fridge is thawed, the beeping should stop.
6. Have a repair person check the circuit board: It is possible that there is an issue with the appliance's circuit board. If so it will most likely need replacement.

Hi!
Please check the troubleshooting part of the manual to this fridge. Hope it will be helpful!
https://manualsbrain.com/en/manuals/1872784/?page=42

Fridge keeps beeping or buzzing: The following is for Frigidaire models but others can be addressed similarly.

Several Frigidaire refrigerator models have an electronic control panel on the freezer door the owner can use to adjust the internal temperature, dispense ice and water and receive notification about issues such as the need to replace a water filter. The refrigerators also emit a beep for various actions and as an occasional alarm. Determining what causes the beeps necessitates some troubleshooting.
Temperature Controls ·A Frigidaire refrigerator's display panel blinks when the control panel is touched to set temperature controls. After pressing "Freezer Temp" or "Refrigerator Temp" on the keypad, press the arrow buttons within five seconds to increase or decrease the desired temperature. If you do not press the arrow buttons within five seconds after pressing "Freezer Temp" or "Refrigerator Temp" on the keypad, the refrigerator beeps to indicate the current setting will stay in place.

Door Open ·When you leave the refrigerator or freezer door open, the refrigerator beeps. Also, the "Door Ajar" indicator illuminates on the appliance's display panel. Shutting the door and pressing "Alarm Reset" stops the beeping and turns off the "Door Ajar" indicator light.
·The Frigidaire refrigerator has a control lock feature that prevents use of its control panel or dispensers when the unit is locked. When the control lock is active, a beep sounds when a keypad or dispenser is pressed. Release the control lock by pressing the "Control Lock" icon for three seconds. A beep will sound, and the icon's light will go out.
Power Reset ·A power reset is occasionally necessary if the Frigidaire refrigerator's control panel does not work normally or a reset function on the keypad does not work. A power reset involves disconnecting power to the refrigerator by unplugging its power cord from the electrical outlet, waiting 30 seconds and plugging the power cord back into the electrical outlet. When the control panel resets, a beep sounds. If the refrigerator beeps even after a power reset and the beeps' source is not known, contact Frigidaire.


Read more :http://www.ehow.com/info_12148688_cause-beeping-noise-frigidaire-refrigerator.
Cause of Beeping Noise in Frigidaire Refrigerator eHow

Often these have door alarms. If the door isn't completely sealed shut then it will alarm and cause the temperature/thermostat to blink to warn of "warm" temperature inside the fridge

Temperature alarm
If the temperature becomes too warm, an alarm will sound and the temperature display will flash. The temperature the appliance is set at will determine when the alarm is triggered.
The alarm will sound and the display will flash under the following conditions:

• - whenevertoomuchwarmairflows into the appliance, for example when food is being loaded, re-arranged, or taken out.
• - wheneverlargeamountsoffoodare being frozen at once.
• - whenevertherehasbeenalengthy interruption of the power supply. Door alarm
  If the appliance door is left open for longer than approx. 60 seconds, the alarm signal will sound.

Switching the alarm system ON
The alarm system is always active. It does not need to be switched on manually.
Switching the alarm OFF early
Once the set temperature has been reached in the freezer section, the alarm signal stops and the temperature display stops blinking. If the alarm signal bothers you, it can be switched off early.
^ Press the alarm off button. The alarm signal will stop. The temperature display will continue to blink until the set temperature has been reached. The display then stops blinking, and shows a steady reading. At this point, the alarm system is ready again if needed.

It is probably no more expensive than a CONTROL BOARD...
POSSIBLY as cheap as a door switch...

It is sensing a DOOR ALARM... and quite reasonably
stopping ... and alarming.

You need to find the PIZZA box, poor door alignment
or FAULTY circuitry that is causing the ALARM.

ELSE
Contact the maker for support
(on your back panel... or by reading your Owners Manual).

Like (example)...
Fisher Paykel E331T Installation Instructions And User Manual Page 44

Hope this helps

Carnac the Magnificent

Hi Clair, thank you for allowing me to assist you.

When the refrigerator is beeping or buzzing, it may be a warning sign of a possible malfunction or an unsafe, interior temperature. To silence the buzzer, you can depress the ALARM OFF button. However, if you have already done this, try unplugging the unit or flipping the household circuit breaker for about ten minutes.

If the alarm continues, it could possibly be experiencing a communication problem with the temperature control/board or wiring failure. I would recommend connecting with a professional appliance tech for a clear-cut diagnosis.

Is the compressor kicking on?

Is your circulating fan working?
Sometimes they stick and need a shot of WD 40 and then work
it back and forth a little until it wants to take off again. Keep me informed
and PLEASE give a Thumbs Up for the effort. The Raz Shack

so what is your question