Based on thin plate theory and thermal conduction equation in view of deformation effect， the thermoelastic coupling model of annular plate and the corresponding motion differential equation of friction plate in the friction clutch is established. The differential equation and the boundary condition are discretized by the differential quadrature method. The relation curves of the first three dimensionless natural frequencies of friction plate in friction clutch with the dimensionless angular velocity and the dimensionless thermolelastic coupling coefficient are obtained in a variable transverse temperature environment. The result shows that the first three dimensionless natural frequencies of friction plate increase with the increase of the dimensionless angular speed and the dimensionless thermolelastic coupling coefficient， and the different boundary conditions have a certain different effect on the increase of natural frequencies of friction plates， which provide the theoretical basis for design and performance analysis of friction clutch.