Backstage sources suggest that the compression necessary for fusing the positively charged nuclei in starship reactors is achieved by "fusion initiators" (TNG Tech Manual pp.76-77), resulting in a "conventional P-P fusion reaction". This creates a "standing pulsed fusion shock" which supposedly keeps up the compression.
This is all backstage talk, not evident on screen. Even then, we have no idea whether the proton-proton fusion there involves high or low temperatures, or how the initiators are supposed to work. Forcefield compression to high pressure? Phaser pulses to high temperature? Something more conventional, or more exotic? For all we know, the fusion process might be a refined and elegant one, indeed "cold" by today's standards.
Timo Saloniemi