While progress in fusion research continues with magnetic and inertial confinement, alternative approaches-such as Coulomb explosions of deuterium clusters and ultrafast laser-plasma interactions-also provide insight into basic processes and technological applications. However, attempts to produce fusion in a room temperature solid-state setting, including `cold' fusion and `bubble' fusion, have met with deep scepticism. Here we report that gently heating a pyroelectric crystal in a deuterated atmosphere can generate fusion under desktop conditions. The electrostatic field of the crystal is used to generate and accelerate a deuteron beam (> 100keV and >4nA), which, upon striking a deuterated target, produces a neutron flux over 400 times the background level. The presence of neutrons from the reaction D + D --> 3He (820keV) + n (2.45MeV) within the target is confirmed by pulse shape analysis and proton recoil spectroscopy. As further evidence for this fusion reaction, we use a novel time-of-flight technique to demonstrate the delayed coincidence between the outgoing α-particle and the neutron. Although the reported fusion is not useful in the power-producing sense, we anticipate that the system will find application as a simple palm-sized neutron generator.