Dirichlet’s task for unstable heat change in stream of hot liquid which travel into infinitely length radial-divergency canal is solved. Are written equation of energy for moving of hot liquid stream and expression for velocity of stream in cilindric coordinates. Is taken in consideration the canal simmetration along axis , heatexhange by heat conduction and convection along axis and by heat conduction along axis . In result were obtained correlations for calculation of temperature field and local heat streams on the walls of canal. The solutions is written by trigonometric, exponential and bessel’s functions. It are used bessel’s functions of second kind real and imaginary arguments fractional number of order.