The results of f_1v_rigid_temp c_rigid_ke c_rigid_rot by the method A.(fix 1 RIGID rigid/small) are :
300 ,300.*** .240., 213.*

,but by the other method B(fix 1 RIGID rigid/nve/small) are
300, 0 , 0, 0
The problems are why the results of rigid temp,translation,and rotational Ke by method B(fix rigid/nve/small) are always zeros? Is the method B(rigid/nve/small)able to calculate correct rigid temp, Ke (and rotational Ke ) ?

In my case,I followed your suggestions to calculate rigid temperatures,
translation Ke,rotational Ke by fix rigid/nve/small and fix rigid/small as
follow,

The results of f_1 v_rigid_temp c_rigid_ke c_rigid_rot by the method A.(fix
1 RIGID rigid/small) are :
300 ,300.*** .240.**, 213.***
,but by the other method B(fix 1 RIGID rigid/nve/small) are
300, 0 , 0, 0
The problems are why the results of rigid temp,translation,and rotational Ke
by method B(fix rigid/nve/small) are always zeros?

this is due to a bug in the two computes, which are not correctly
identifying fix rigid/nve/small as a style derived from fix
rigid/small.

and then recompile your LAMMPS executable with them, or you'll have to
wait until the bugfix propagates into the official source or
precompiled binaries.