Hi we went in January last year and it was comfortably warm. T shirts and shorts for the day, we did have one day of torrential rain in St Thomas so we had to use our macs for about an hour and couldn't get 'downtown' because of flooding but other than that it was definately summer.
Enjoy your cruise.
We have been to the Caribbean in January and February and each time it has been hot during the days. If there has been a storm it is over very quickly. We have never needed any sort of jumper during the days at all. Each time we've been to St. Lucia we have had brief rain but it didn't last long.
You should expect the temperature to be in the high 20s'C (low 80s'F), this is peak season and generally perfect weather. .... Neil.