ABSTRACT We report the results of new XMM-Newton observations of the middle-aged (τc = 1.1 × 105 yr) radio pulsar PSR J1740+1000 carried out in 2017–2018. These long pointings (∼530 ks) show that the non-thermal emission, well described by a power-law spectrum with photon index Γ = 1.80 ± 0.17, is pulsed with a ∼30 per cent pulsed fraction above 2 keV. The thermal emission can be well-fit with the sum of two blackbodies of temperatures kT1 = 70 ± 4 eV and kT2 = 137 ± 7 eV, and emitting radii $R_1=5.4_{-0.9}^{+1.3}$ 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 (∼67 ks) of this pulsar carried out in 2006. The X-ray thermal and non-thermal components peak in antiphase 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, disfavours 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 at different temperatures shows that the ratios T2/T1 and R2/R1 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.