To accomplish this you are going to need to use python, which you could then create a script tool from and use in model builder. Below is a code sample. Basically we are opening the MXD, gettting some references to the data frame and layers and then stepping through time. At each step we perform our analysis and then move to the next time step.
#Get a reference to the map document and first data frame
mxd = arcpy.mapping.MapDocument('Current') #If code is run in the app with the MXD open, otherwise pass the path to the MXD
df = arcpy.mapping.ListDataFrames(mxd)[0] #Assuming here there is only one data frame in the MXD
rasterLayerName = "SST" #replace with name of netCDF raster layer
rasterLayer = arcpy.mapping.ListLayers(mxd, rasterLayerName, df)[0]
hurricaneLayer = "Hurricanes" #replace with name of hurricane layer
hurricaneLayer = arcpy.mapping.ListLayers(mxd, hurricaneLayerName, df)[0]
#Loop through each time step within the full time extent
df.time.currentTime = df.time.startTime
while df.time.currentTime <= df.time.endTime:
#Add your logic here, I assume you are using extract values to point
#So we don't overwrite the output each time, we need a unique name, this will append the Year and Month value currently being processed.
uniqueName = "Hurricanes_" + dt.time.currentTime.strftime("%Y_%m")
outPointFeatures = r"C:\OutputDate\" + uniqueName
ExtractValuesToPoints(hurricaneLayer, rasterLayer, outPointFeatures,
"NONE", "VALUE_ONLY")
#Set the current time of the data frame to the next time step
df.time.currentTime += df.time.timeStepInterval
