Context. Pulsating thermal X-ray emission from millisecond pulsars can be used to obtain constraints on the neutron star equation of state, but to date only five such sources have been identified. Of these five millisecond pulsars, only two have well-constrained neutron star masses, which improve the determination of the radius via modelling of the X-ray waveform. Aims. We aim to find other millisecond pulsars that already have well-constrained mass and distance measurements that show pulsed thermal X-ray emission in order to obtain tight constraints on the neutron star equation of state. Methods. The millisecond pulsar PSR J1909–3744 has an accurately determined mass, M = 1.54 ± 0.03 M_⊙ (1σ error) and distance, D = 1.07 ± 0.04 kpc. We analysed XMM-Newton data of this 2.95 ms pulsar to identify the nature of the X-ray emission. Results. We show that the X-ray emission from PSR J1909–3744 appears to be dominated by thermal emission from the polar cap. Only a single component model is required to fit the data. The black-body temperature of this emission is $ {kT}=0.26^{0.03}_{0.02} $ keV and we find a 0.2–10 keV un-absorbed flux of 1.1 × 10⁻¹⁴ erg cm⁻² s⁻¹ or an un-absorbed luminosity of 1.5 × 10³⁰ erg s⁻¹. Conclusion. Thanks to the previously determined mass and distance constraints of the neutron star PSR J1909–3744, and its predominantly thermal emission, deep observations of this object with future X-ray facilities should provide useful constraints on the neutron star equation of state.