Acu-Rite indoor outdoor thermometer won't stop periodic beeping

The book for that unit is here: http://www.acurite.com/kbase/search/query/00754/

This is a link to your manual:

AcuRite 75321A1 Instruction Manual

Dave

Before attempting to set the time, let the outdoor transmitter sync with the indoor receiver. Once that's done, you'll be able to successfully set and retain the date and time.

http://www.partshelf.com/acu-rite-instruction-manuals.html

Double check the batteries and the direction in which they are installed. If there is one backwards in the sending unit that is outside, it will not send a signal. Also, there is typically one battery in the indoor unit that is responsible for receiving the signal from the outdoor unit. If all of the batteries are in correctly except that battery, you will see the display, but will not get the data transmitted from the outside sending unit.

Its a remote temperature sensor to read a aquarium or refridgerator or pool water temperature

take a look at Chaney Instruments http://diplodocs.nl/references.php

Wireless Thermometer with Sensor
Model 00735 ??

There is no way to turn off beeping. From this site: http://www.chaneyinstruments.com/FAQ.aspx
found solution - Q: My wireless weather station periodically beeps, why?
A: Make sure that any alert and/or alarm features are deactivated first. Constant, sporadic beeping is generally due to the unit's ability to detect a foreign radio frequency of another wireless unit when that unit transmits a signal. Wireless devices that may cause beeping but are not limited to these devices are; scanners; computers w/wireless keyboard/mouse; or other wireless weather instruments. Essentially, any wireless devices transmitting on a radio frequency have the potential to interfere with each other. Limit the amount of wireless devices to lesson the chance of interference. When beeping occurs, one device will need to be deactivated.

Another external temp gauge showed up on the other channel, so my neighbor or someone is using the similar unit. MY SOLUTION: opened back of case and cut black wire to piezo speaker (at base if rear cover opposite side of stand-up prop) that creates beep. ALL good now.

I had the exact same problem, and found the answer on the Chaney Instrument FAQ page. There's no real solution, but here is the explanation:
Q: My wireless weather station periodically beeps, why?
A: Make sure that any alert and/or alarm features are deactivated first. Constant, sporadic beeping is generally due to the unit’s ability to detect a foreign radio frequency of another wireless unit when that unit transmits a signal. Wireless devices that may cause beeping but are not limited to these devices are; scanners; computers w/wireless keyboard/mouse; or other wireless weather instruments. Essentially, any wireless devices transmitting on a radio frequency have the potential to interfere with each other. Limit the amount of wireless devices to lesson the chance of interference. When beeping occurs, one device will need to be deactivated.