I think this would be easy in Python. If all of your rasters are in the same folder you could just use the ListRasters to iterate through them all. If not, you could use a wildcard and the os.walk or arcpy.da walk (for Arc 10.1) to loop thru folders.
import arcpy, os
arcpy.env.workspace = r'G:\WIU\Geog408\deng_lab4\Thermal_south_results\May\deg_170'
arcpy.env.overwriteOutput = True
# Clip region
poly = r'C:\testing\TestData\clipReg.shp'
out_folder = r'C:\testing\TestData\outputs'
for raster in arcpy.ListRasters():
out_raster = os.path.join(out_folder,raster)
print 'Clipped: %s' %raster