Steven,
I buy most vaccine directly from Sanofi. Our Sanofi rep supplied me with a continuous temperature monitor. It is a glycol filled bottle with a thin wire that runs to the outside of the refigerator where the digital display is mounted. It continuously monitors and has high/low alarms. I don't know that you can print a log, but it does store history. So, you might check with your vaccine supplier to see if they offer such.