The fresh modification of the numerical method based on the Full Lagrangian 
Approach (FLA) is developed for calculation of particle-phase flow field in 
dilute gas-particles mixture flows. The collisionless "gas" of particles is 
treated as the continuum for which all basic equations including the continuity 
equation, the momentum equation and the energy equation are written in the 
Lagrangian coordinates. (The majority of researchers do not use the continuity 
equation in an explicit form changing it by some approximate relations. Such 
approach is also known as the Lagrangian one but it is not the FLA, of course.) 
When using the FLA one must calculate the components of the Jackobian of the 
Eulerian/Lagrangian transformation to obtain the density of the dispersed phase 
along particles' trajectories from the continuity equation. These components can 
be calculated by different ways, but in the present paper they are calculated by 
numerical differentiation of the Eulerian coordinates with respect to the 
Lagrangian ones using particles' parameters on several close trajectories. This 
way has advantages over any other one if the right-hand sides of the momentum 
and energy equations for a particle are very cumbersome. Such situation takes 
place for fine particles moving inside the non-isothermal boundary layer because 
of very complicated gas-particle interaction in this case, and it is studied in 
the paper. The developed method provides very high spatial resolution.