RE: average temperature
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Our official index that tracks ENSO does use a de-trending process in an attempt to remove long-term trends.
http://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ONI_v5.php
More detailed description here:
http://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ONI_change.shtml