Temperature data are a primary #welltest measurement (i.e. not calculated like pressure data) and should be examined for quality control and anomalies. Temperature data are a good indicator of wellbore and reservoir characteristics.
Joule-Thompson cooling usually dominates flowing temperatures in gas wells (#LNG) as a function of gas expansion through pore throats or perforations. If the magnitude of cooling decreases (becomes less cool) then the near wellbore region might be cleaning up.
With recorders landed above the formation, temperatures warming usually indicates liquid loading (i.e. liquid from the formation warms the gauges up). One anomaly to watch for immediately after shut-in is a spike in temperature indicating adiabatic heating (a gas compression phenomenon).