The approximate gradient index is formed under the condition of electromagnetically induced transparency (EIT) in the hot atomic medium. Theoretical study shows that, self-imaging can also be induced after considering Doppler broadening. With the split-step Fourier medthod and lattice matrix, normalized intensity distribution on the transverse transmission plane is studied. With the definition of difference factor of image plane, the location of the self-imging can be calculated accurately. The influences of the temperature on the position of the self-imaging and the corresponding imaging quality are discussed in detail. Numerical results show that, with the increase of the temperature, the location of the self-imaging linearly moves away from the original object, and the self-imaging quality decreases.