The theory of collective pinning in the presence of thermal fluctuations of vortex lines is developed. Critical current jc is shown to decrease rapidly with temperature. Flux creep under the action of weak (j << jc) current is considered and j-dependence of the effective energy barrier U(j) is estimated. At the current decrease U(j) grows initially as j-α, and then saturates at a finite value Upl, due to plastic deformations coming into play. The relations is discussed between this theory and the existing experiments.