  We report the results of new XMM-Newton observations of the middle-aged
($\sim$10$^5$ yr) radio pulsar PSR J1740+1000 carried out in 2017-2018. These
long pointings ($\sim$530 ks) show that the non-thermal emission, well
described by a power-law spectrum with photon index $\Gamma=1.80\pm0.17$, is
pulsed with a $\sim$30% pulsed fraction above 2 keV. The thermal emission can
be well fit with the sum of two blackbodies of temperatures $kT_1=70\pm4$ eV,
$kT_2=137\pm7$ eV, $R_1=5.4_{-0.9}^{+1.3}$ km and $R_2=0.70_{-0.13}^{+0.15}$ km
(for a distance of 1.2 kpc). We found no evidence for absorption lines as those
observed in the shorter XMM-Newton observations ($\sim$67 ks) of this pulsar
carried out in 2006. The X-ray thermal and non-thermal components peak in
anti-phase and none of them is seen to coincide in phase with the radio pulse.
This, coupled with the small difference in the emission radii of the two
thermal components, disfavors an interpretation in which the dipolar polar cap
is heated by magnetospheric backward-accelerated particles. Comparison with the
other thermally-emitting isolated neutron stars with spectra well described by
the sum of two components shows that the ratios $T_2$/$T_1$ and $R_2$/$R_1$ are
similar for objects of different classes. The observed values cannot be
reproduced with simple temperature distributions, such as those caused by a
dipolar field, indicating the presence of more complicated thermal maps.
