You could use the watchdog timer to wake yourself up every 8 seconds or so and then read the state of the pin. Then count the number of 8 second sleeps that occur with the temperature above 100C. When the temperature goes back below 100C, write the count to the next free EEPROM location.
If you use 1 byte per time period above 100C, then the 8 second WDT counter will give you 255 x 8s period (or 2040 seconds, 34 minutes).
A 328P has 1024 bytes of EEPROM so that will allow you to record 1024 time periods. At 1 per day, that's > 2.5 years of values.
That would be the micro going to sleep before the serial buffer has emptied, as @Budvar10 says.
I did experiment some time ago regarding the "accuracy" of the WDT and it's not that bad and likely perfectly good enough for your application, give that the WDT isn't meant to be used for any form of accurate timing.