  Aims. We analyse unpublished Spitzer observations of the thermal phase-curve
of WASP-121 b, a benchmark ultra-hot Jupiter. Methods. We adopted the wavelet
pixel-independent component analysis technique to remove challenging
instrumental systematic effects in these datasets and we fit them
simultaneously with parametric light-curve models. We also performed
phase-curve retrievals to better understand the horizontal and vertical thermal
structure of the planetary atmosphere. Results. We measured planetary
brightness temperatures of $\sim$2700\,K (dayside) and $\sim$700--1100\,K
(nightside), along with modest peak offsets of 5.9$^{\circ} \pm$1.6
(3.6\,$\mu$m) and 5.0$^{\circ}$$_{-3.1}^{+3.4}$ (4.5\,$\mu$m) after
mid-eclipse. These results suggest inefficient heat redistribution in the
atmosphere of WASP-121 b. The inferred atmospheric Bond albedo and circulation
efficiency align well with observed trends for hot giant exoplanets.
Interestingly, the measured peak offsets correspond to a westward hot spot,
which has rarely been observed. We also report consistent transit depths at 3.6
and 4.5\,$\mu$m, along with updated geometric and orbital parameters. Finally,
we compared our Spitzer results with previous measurements, including recent
JWST observations. Conclusions. We extracted new information on the thermal
properties and dynamics of an exoplanet atmosphere from an especially
problematic dataset. This study probes the reliability of exoplanet phase-curve
parameters obtained from Spitzer observations when state-of-the-art pipelines
are adopted to remove the instrumental systematic effects. It demonstrates that
Spitzer phase-curve observations provide a useful baseline for comparison with
JWST observations, and shows the increase in parameters precision achieved with
the newer telescope.
