Best temperature storage IC? EEPROM or SRAM IC
You may be thinking of battery-backed static RAM. Such a thing does exist, and can be used as an alternative to EEPROM. EEPROM chips typically have a limited number of writes before they become read-only. That number is in the tens or hundreds of thousands per location, so that lifetime may not be a meaningful limitation, depending on your application. But if you must frequently log a value and must always be sure to get the most frequently logged value, and if that means that your EEPROM will have too short a lifespan, then you may have no choice but to use BBSRAM instead. The only limitation there is the amount of powered-off time your battery and chip combination will allow, and whether than exceeds your needs (if not, you will lose data).