I need to know if there is any precipitation and temperature GIS data for these islands.
Federated States of Micronesia
Northern Mariana Islands
Republic of Palau
The US Territories have weather stations, so you can get point-based data for temperature, precipitation, etc by station from NOAA. If you choose the CSV format and check the geographic location option to get coordinates, you'll be able to plot the data.
For some reason the US Territories don't show up as a filter option in the standard search tool (under Discover Data by menu - blue box). But they do in the Data Tools (red box) or you can use the mapping tools to draw an area. The red Data Tools box seems easiest; select it, then choose the Select by Location option, and you'll be able to filter by US Territories and select the ones you want. You can grab all the stations in that area and then choose your options for dataset, format, year, geographic locations (to get coordinates), etc.