We have predicted theoretically and detected in laboratory experiments a tangling clustering of inertial particles in a stably stratified turbulence with imposed mean vertical temperature gradient. In the stratified turbulence a spatial distribution of the mean particle number density is nonuniform due to the phenomenon of turbulent thermal diffusion, i.e., the inertial particles are accumulated in the vicinity of the minimum of the mean temperature of the surrounding fluid, and a nonzero gradient of the mean particle number density, N, is formed. It causes generation of fluctuations of the particle number density by tangling of the large-scale gradient N by velocity fluctuations. In addition, the mean temperature gradient T produces the temperature fluctuations by tangling of the large-scale gradient T by velocity fluctuations. The anisotropic temperature fluctuations contribute to the two-point correlation function of the divergence of the particle velocity field, i.e., they increase the rate of formation of the particle clusters in small scales. We have demonstrated that in the laboratory stratified turbulence this tangling clustering is much more effective than a pure inertial clustering (preferential concentration) that has been observed in isothermal turbulence. In particular, in our experiments in oscillating grid isothermal turbulence in air without imposed mean temperature gradient, the inertial clustering is very weak for solid particles with the diameter of 10 μm and Reynolds numbers based on turbulent length scale and rms velocity, Re=250. In the experiments the correlation function for the inertial clustering in isothermal turbulence is much smaller than that for the tangling clustering in nonisothermal turbulence. The size of the tangling clusters is on the order of several Kolmogorov length scales. The clustering described in our study is found for inertial particles with small Stokes numbers and with the material density that is much larger than the fluid density. Our theoretical predictions are in a good agreement with the obtained experimental results.