The goal of this work is possibility investigation for developing of high efficient and high output power mini TEA CO2 laser Second Harmonic Generators (SHG) applicable to use in mobile gas analysis lidars. Efficiency of SHG with Te, CdGeAs2, ZnGeP2, AgGaSe2 AgIn0.4Ga0.6Se2, Tl3AsSe3, and GaSe nonlinear crystals was estimated by solving shortened equations for interacting waves in combination with thermodynamic one. The latter equation allowed us to take into account the crystal self-heating effect (thermal refraction and lens effect) and inhomogeneous disturbance of SHG phase-matching, as well as took into account an energy transfer from the pumping wave to SH, optical losses, aperture and diffraction effects. In so doing we demonstrate SHG efficiencies using the following CO2 pumping laser parameters: wavelength (lambda) equals 9.3 micrometer, pulse duration (tau) equals 50 ns, pulse repetition rate f equals 1000 Hz, pulse power E equals 50 mJ. The pulse repetition rate satisfies condition of the 'frozen' atmosphere and the energy is sufficiently large for working on topographic targets that are 10 km off using both CO2 laser emission and its SH (the conversion efficiency is from 5 to tens of percent). Besides, we believed that the laser is operated in TEM00 mode, the pumping intensity was assumed to be a half of the threshold pumping intensity (it provides for stable SHO operation), the time shape and intensity distribution in the beam cross section were assumed to be Gaussian. These parameters as a whole correspond to ones of the typical mini TEA CO2 lasers, which are used in mobile lidars. Additional angular tuning of the crystals, that maximizes SHG efficiency, as well as the optimal crystal lengths, giving its absolute maximum for the fixed pumping pulse repetition rate, were also determined.