Nuclear missiles would not deal thermal damage so much as "radiation damage"; i.e. the radiation emitted would mess with many sensors and equipment. The reaction itself may cause more damage than a bog standard explodey missile we're used to now, but ultimately I suspect missiles would all face the same issue: they have to be launched across relatively massive distances against ships that probably have every form of point defense under the sun (if you'll excuse that legendary pun). Should missile-based weaponry appear to become prominent I suspect kinetic/flak screen defenses and scramblers in various forums would become staple, and definitely not restricted to four on a massive ship. Actually, point defense is probably the earliest practical application of lasers in space combat.
With the technology we understand at the moment, the concept behind flak weaponry would probably be prominent. You're probably correct in that it would be launched from projectiles - perhaps similar to what was tried with real life rail guns, whereby the projectile effectively launches shot over a large area. It's easy to shoot a few missiles down; it's not so easy when those projectiles instead launch a wall of metal pieces.
Nuclear reactions do generate a massive amount of thermal energy and light in addition to other forms of radiation. Plus the light and radiation tend to heat up whatever they hit, just like a laser. Just substitute brute force for focus. In fact, once you're done applying your inverse square law you pretty much calculate nuke damage the same way you calculate laser damage, using W/m^2 (though it's likely to end up in MW/cm^2 to produce easier to read numbers).
Remember, the sun is a giant fusion bomb in space and it provides literally all of our heat from 1AU away. Our fusion bombs are smaller, but significantly closer. It's thermal damage.
It's pretty obvious that you're starting with your hatred of missiles and trying to rationalize backwards into a future where they don't exist. Could we theoretically have a future of super amazing point defenses that can cost effectively nullify any incoming missiles? Maybe, we could also have a future of perfect shielding that never breaks and can only be bypassed by melee weapons. But that doesn't prove ranged weapons are impractical in general, it only sets up a contrived future specifically designed to exclude them.
Then there's the fact that any KKV that releases its payload on an intercept course before it reaches the edge of your PD range is now functionally equivalent to an incoming railgun round. Though some might argue that such an early-release warhead might be considered a single-shot drone rather than a missile, definitions get fuzzy when you start piling on tricks.