  We have explored a method for finding giant planets in the outer Solar System
by detecting their thermal emission and proper motion between two far-infrared
all-sky surveys separated by 23.4 years, taken with the InfraRed Astronomical
Satellite (IRAS) and the AKARI Space Telescope. An upper distance limit of
about 8,000 AU is given by both the sensitivities of these surveys and the
distance at which proper motion becomes too small to be detected. This paper
covers the region from 8,000 AU to 700 AU. We have used a series of filtering
and SED-fitting algorithms to find candidate pairs, whose IRAS and AKARI flux
measurements could together plausibly be fitted by a Planck thermal
distribution for a likely planetary temperature. Theoretical studies have
placed various constraints on the likely existence of unknown planets in the
outer solar system. The main observational constraint to date comes from a WISE
study: an upper limit on an unknown planet's mass out into the Oort cloud. Our
work confirms this result for our distance range, and provides additional
observational constraints for lower distances and planetary masses, subject to
the proviso that the planet is not confused with Galactic cirrus. We found 535
potential candidates with reasonable spectral energy distribution (SED) fits.
Most would have masses close to or below that of Neptune (~0.05 Jupiter mass),
and be located below 1,000 AU. However, examination of the infrared images of
these candidates suggests that none is sufficiently compelling to warrant
follow-up, since all are located inside or close to cirrus clouds, which are
most likely the source of the far-infrared flux.
