Or 2014-2015. Dec 22-29 at BOS had four days in the 40s and four days in the 50s and felt like spring.
Jan turned cold by the 5th or so, but still had a day where BOS hit 50 mid-month. It was only Jan 20 that BOS fell below 40 for that 45 day stretch until March 4 (which is the longest on record, IIRC) and then only slowly crept up into the 50s (only four days in the 50s in March, which is basically the same pattern with a lot more sun). But that is absolutely the exception, and given that patterns usually last a significantly shorter time, a few days in the 40s or 50s should be expected in January.
Checking out the NOW data, there have been 21 Januarys where the temperature has stayed below 50 for the entire month since 1872. So one out of every 7-8 years doesn't have a thaw that breaks 50. As for months that stay below 40, that's happened twice: Jan, 1875 and Feb, 2015.