I'd recommend taking out the batteries and letting it naturally warm back up to room temperature, with the back cover off. Once it's reached room temperature again, try placing it up against a fan (again, with the back cover off and batteries removed), in case water has built up inside from being frozen and "thawing." During this time, don't turn it on at all in case there is moisture inside. I'd suggest keeping it in front of the fan and turned off for at least 24 hours, if not 48 hours. You may also want to flip the Tamagotchi every several hours.
Alternatively, you could also try placing the Tamagotchi in rice to absorb the moisture, instead of in front of a fan (I'd recommend keeping the back cover on for this so you don't get rice inside...), but personally, this method has never worked as well for me as simply using a fan.
Hopefully this helps! I've had similar occurrences in the past, along with water damage, and this will usually fix it up.