  In this paper, we study a critical exponent to the semilinear heat equation
with forcing term on Heisenberg group. Our technique of proof is based on
methods of nonlinear capacity estimates specifically adapted to the nature of
the Heisenberg group. Surprisingly, the critical exponent will be bounded for
all dimensions of the Heisenberg group, in contrast to the Euclidean case which
in the 1D and 2D cases will be infinite. In addition, we give an upper bound
estimate on the lifespan of local solutions.
