Yep, January weather can fluctuate wildly, even within the same week. Bring your swimsuit, shorts and sunblock, and also a warm jacket, warm socks, gloves, and a hat!
Seriously, layers are your friend! I went on a trip in October a few years ag. because it was a longer trip (12 days) I looked at the forecast and saw it was supposed o be in the 90s the first week. So I packed nearly all shorts, sleeveless tops, and sandals. We had a cold snap on Day 8 (temps droped about 30 degrees overnight!), and I really, really wished I had packed more warm clothes.
The moral of my stry is that I now pack a little bit of everything, even at times of the year when it's "always" _________ (filll in the blank). It's a pain, not to mention very expensive, to have to buy things like gloves, a warm sweatshirt, etc. -- especially when I have all of that stuff at home!