They must not radiate heat. They’d be impossible to hold. But if they were to hit metal or something, that would radiate heat as it were being melted/cut.
The way they get swung implies that their center of gravity is not in the handle – it’s somewhere down the ‘blade’ – so the light saber blade itself must have some mass.
The blades also must have some kind of volume – they exclude each other, when Jedi or Sith swing them at each other, the blades don’t pass through one another. Also ‘blaster’ shots bounce off them, so they have both mass and volume.
Now I’m assuming conservation of mass and energy is still in effect here – but if so, a powered-off lightsaber should weigh as much as a powered-on one. I’ll take the fact that they’re not portrayed in the movies this way as a simple technical flub.
They don’t need ‘guards’ on them – perhaps the blades ‘stick’ when they hit each other so there is no risk of the blade sliding down another and chopping off an unsuspecting Jedi’s digits.
The way the blades seem to be able to cut off heads, hands, etc make them seem more like a ‘point’ of laserness, as opposed to the inch-or-so of diameter that they appear as. Maybe the force (lowercase f, not uppercase F) which excludes the other light saber (and perhaps also deflects blaster shots) is that inch, inch-and-a-half, but the cutting part is perhaps much narrower. This would have to be the case because to cut off someone’s hand or head, you’d have to burn through an inch thick of flesh, and that would take some serious effort, and once done, the heat that would come off the guy who got cut might even burn you!
Problem with this theory is that in SW ep. I, Qui-Gon Jinn jams his light saber into a shutting blast door to melt his way through, which it begins to do. He does have to wiggle it around a little to start cutting through, so maybe my theory is working after all.