We surveyed the global temperature field of Saturn’s atmosphere using the Cassini Composite Infrared Spectrometer (CIRS, 7-1000 µm), complemented by ground-based mid-infrared observations (7-25 µm), from 1995 to 2020. We detected and characterized properties of slowly moving zonal thermal waves and their variability during that period. The most inclusive CIRS surveys, FIRMAPs (15 cm-1 spectral resolution), covered the planet from the equator to either north or south pole, sweeping through the latitude range while the planet rotated beneath over its ~10-hour rotation. Additional measurements were made by ground-based observations at the Infrared Telescope Facility using the MIRSI instrument, the Very Large Telescope using VISIR and the Subaru Telescope using COMICS. We sampled spectral ranges dominated both by upper-tropospheric emission (80-200 mbar) and by stratospheric emission (0.5-3 mbar). Several types of slowly moving zonal thermal waves were detected: (1) meridionally broad wavenumber-1 through -3 oscillations, (2) equatorial waves, some of which extend northward to mid-latitudes, (3) prominent wavenumber-12 oscillations in the southern hemisphere, which also have components of wavenumbers 1 through 3 and extend over 15°-35°S latitude, (4) mid-latitude wavenumber > 2 oscillations in both hemispheres with variable time dependence and morphology, and (5) discrete low-latitude tropospheric features. The prominent southern-hemisphere waves appear to have distinct periods of maximum intensity around 2003-2004 from ground-based observations and 2008-2009 from CIRS FIRMAPs. These waves are easily detectable in both the stratosphere, where the other types of waves are prominent, but also in the troposphere with no detectable phase shift in longitude. These waves were also sufficiently coherent to track a mean phase speed, which is about 0.5° per day, retrograde. After 2009, wavenumber-1 oscillations in the northern hemisphere are joined by higher-wavenumber oscillations. A local temperature maximum is seen around 2010-2011, then another in 2016-2017. Further ground-based observations are required to determine whether the amplitude of northern-hemisphere waves is influenced by seasonally dependent insolation.