I've mentioned this subject briefly on various different occasions in one of my many, many laser cheerleading posts on this site passim ad nauseam. I'll gloss over the issue of high-temperature thermal superconductors here... they're unobtanium, in the sense of "we could establish plausible physical properties of this material, but it probably can't exist in real life". That category includes the stuff that holds wormholes open or makes Alcubierre warps possible, and so it is fair game for even reasonably hard scifi.
If your thermal superconductors somehow had infinite thermal conductivity, they'd resist purely thermal effects quite well, up to the capacity of your heatsinks and/or radiators. Obviously you could just cook a target by pouring more energy into it than it can dump, but that's probably not going to be generally practical... it should work on smaller targets, like missiles, but not very large things. With finite conductivity, you just have to deliver enough heat to a small enough space in a short enough period of time that the superconductor will vaporize before it can conduct it away, so a powerful enough heat source can defeat your armor.
The problem is that sufficiently intense laser light isn't just heat.
Short wavelength lasers, which mostly means vacuum UV and up (a 10 eV ionization energy corresponds to ~124 nm wavelength), ionize matter they illuminate and ionization is not a thermal effect. Your thermal superconductors, if they are made of matter, will not necessarily cope well with this sort of thing that can disrupt crystal structures and molecular composition and all sorts of things that superconductivity probably needs in order to work nicely.
Nuclear pumped lasers are one possible source of this sort of radiation, which implies a surprisingly low tech-level by the standards of having-warfare-in-space scifi... humans could probably make them now (project excalibur demonstrated the technique in 1980 as part of the guardian dauphin nuclear test) though they'd be quite expensive, I suspect. They're only pulsed by the nature of their pump source, so maybe they don't count, though. A free electron laser might also do the job... they already exist, though current examples are not at all suitable for weapons. You might reasonably find a way to shrink an accelerators right down whilst maintaining efficiency in a scifi setting, though that will be challenging in real life (wakefield accelerators are tiny, but very low efficiency making them poorly suited for weapons).
With sufficiently intense laser illumination, even using non-ionizing wavelengths, you can get nonlinear optical effects like multi-photon absorption which in turn can cause ionization if the total energy absorbed is sufficient (obviously this works better if the laser is short wavelength). Once those electrons have left the vicinity, the now positively-charged nuclei left behind will repel each other in an effect called a Coulomb explosion, and that's the end of your nice material structure and probably your thermal superconductivity, too.
Now, sufficiently intense is doing some heavy lifting there. From the wikipedia article on Coulomb explosions:
Coulomb explosions for industrial machining are made with ultra-short (picosecond or femtoseconds) laser pulses. ...enormous beam intensities [are] required (10–400 terawatt per square centimeter thresholds, depending on material)
That's a big ask, but not an impossible one.
This all means that if your thermal superconductor is made of matter, it cannot guarantee safety against laser weapons, though it will significantly reduce the effective range of lasers emitting non-ionizing wavelengths. It is unlikely to help much against VUV, x-ray or gamma-ray emitting weapons. You should also consider that the existence of thermal superconductors makes it easier to construct unreasonably powerful lasers.
If your tech-level precludes nuclear-pumped lasers and picosecond pulse generation, then thermal superconductors seem likely to render laser weapons significantly less useful.