fix rigid

In my case, it is that the copper particles are immersed in water. I want to calculate the themal conductivity with the MP algorithm .However, the fix rigid command cannot control the temperature. Without a fix rigid command, the shape of the particles is no longer a primitive sphere.I also controlled the particle temperature with the fix rigid / nvt / mall .Can you tell me how you solved such a difficult problem?
Hope your reply!

what is water model that you have used in your simulation

fix rigid does allow to set a (langevin) thermostat. please re-check the documentation.
beside that, a) by making your nano particles rigid objects, they contribute very few degrees of freedom to the total system and after a sufficient equilibration, you can just run them without a thermostat without having to worry much about errors: they will still exchange energy with the solvent which is thermalized. b) if your nanoparticles do not maintain their shape (but should), then there may be something wrong with your model or potential or settings, or by forcing a specific shape you are ignoring the physics of the material you are using.

in short, i think there are some more fundamental problems you need to work out and spend more time reading documentation.