user6888: i am building an outdoor sensor with a combination of a custom Arduino board and a battery (+solar charging). I experience strange behavior when the temperature falls below a certain value (i can reproduce it by putting it in the freezer), regardless which type of battery i am using. The custom Arduino runs without power-regulation, straight from the 3.7volts the battery can provide. 
How can i prevent this to happen? I guess a little heating would be not really a solution as i am trying to consume as less energy as possible.
Would a (step up) regulator possibly help? Any other ideas?
---Update---
Thanks to your comments here i figured out, that the AVR 328p should not be operated below a voltage of 3.7v if run at 16Mhz. As i am running with a 3.7v LiPo Battery that could easily explain my problem i guess. My first try to decrease the processor speed to 8Mhz with a Prescaler worked, but the GSM Fona does not seem to like it. So i would like to try something in between like 10Mhz or 12Mhz. As the prescaler does not support this, my question is: can i just use another crystal or would i have to modify something in the code/bootloader as well?

user630: To answer your modified question:
Running the ATmega328p at 16Mhz with 3.7v is out of spec - see this EESE answer for reference or the ATmega datasheet - so the obvious solution would be to lower its speed to 8Mhz.
But since you also mentioned that there is an additional GSM breakout board involved (Adafruit Fona), which expects UART (in auto-baud mode) Rx/Tx connection, it might not be that trivial. Further exploration of the Fona library's source code reveals that it has several hard-coded delays (see Adafruit_FONA.cpp::begin, for example), but its core seems to be implemented inside the Adafruit_FONA::readline method, which uses an underlying Stream, which in turns comes from a Software/Hardware serial object, as shown in the FONAtest.ino example that comes with the library. 
From my experience, Software/Hardware serial should work fine on 8Mhz, except maybe when using high baud rates, which is solvable. 
The hard-coded delays doesn't look like they should cause actual damage except for delay, but you could cut them in half just to see if you can make the library work.
Additional aspect that you should consider is the comment from Adafruit's Fona product page, regarding pin Vio:

This is the pin that you MUST drive with an external voltage from
  3V-5V to set the logic level converter

So, despite that from the datasheet, the Fona seems to have a voltage regulator, you might still want to consider adding a decoupling capacitor between Vcc and Gnd of your battery, to  mitigate transient current draws from any component in your circuit. 

6888: <p>i am building an outdoor sensor with a combination of a custom Arduino board and a battery (+solar charging). I experience strange behavior when the temperature falls below a certain value (i can reproduce it by putting it in the freezer), regardless which type of battery i am using. The custom Arduino runs without power-regulation, straight from the 3.7volts the battery can provide. 
How can i prevent this to happen? I guess a little heating would be not really a solution as i am trying to consume as less energy as possible.
Would a (step up) regulator possibly help? Any other ideas?</p>

<p>---Update---
Thanks to your comments here i figured out, that the AVR 328p should not be operated below a voltage of 3.7v if run at 16Mhz. As i am running with a 3.7v LiPo Battery that could easily explain my problem i guess. My first try to decrease the processor speed to 8Mhz with a Prescaler worked, but the GSM Fona does not seem to like it. So i would like to try something in between like 10Mhz or 12Mhz. As the prescaler does not support this, my question is: can i just use another crystal or would i have to modify something in the code/bootloader as well?</p>
 630: <p>To answer your modified question:</p>

<p>Running the ATmega328p at 16Mhz with 3.7v is out of spec - see <a href="https://electronics.stackexchange.com/questions/58818/programming-3-3v-atmega328-running-at-16mhz">this EESE answer</a> for reference or the ATmega datasheet - so the obvious solution would be to lower its speed to 8Mhz.</p>

<p>But since you also mentioned that there is an additional GSM breakout board involved (Adafruit Fona), which expects UART (in auto-baud mode) Rx/Tx connection, it might not be that trivial. Further exploration of the Fona library's source code reveals that it has several hard-coded delays (see <code>Adafruit_FONA.cpp::begin</code>, for example), but its core seems to be implemented inside the <code>Adafruit_FONA::readline</code> method, which uses an underlying <code>Stream</code>, which in turns comes from a Software/Hardware serial object, as shown in the <code>FONAtest.ino</code> example that comes with the library. </p>

<p>From my experience, Software/Hardware serial should work fine on 8Mhz, except maybe when <a href="http://forum.arduino.cc/index.php?topic=212962.0" rel="nofollow noreferrer">using high baud rates</a>, which is solvable. 
The hard-coded delays doesn't look like they should cause actual damage except for delay, but you could cut them in half just to see if you can make the library work.</p>

<p>Additional aspect that you should consider is the comment from Adafruit's Fona product page, regarding pin <strong>Vio</strong>:</p>

<blockquote>
  <p>This is the pin that you MUST drive with an external voltage from
  3V-5V to set the logic level converter</p>
</blockquote>

<p>So, despite that from the datasheet, the Fona seems to have a voltage regulator, you might still want to consider adding a decoupling capacitor between Vcc and Gnd of your battery, to  mitigate transient current draws from any component in your circuit. </p>
