Newbie Project: Arduino Ear Thermometer using Thermopile

In that case you are talking about 86400 to 172800 readings. Even at a byte each, that is far more than the available EEPROM (1 Kb).

You could scale down a bit (a reading every couple of minutes) or get some external storage. An SD card in a small adapter might do the trick, eg.

Or an EEPROM chip, eg.