  In this paper we prove local well-posedness in Orlicz spaces for the
biharmonic heat equation $\partial_{t} u+ \Delta^2 u=f(u),\;t>0,\;x\in\R^N,$
with $f(u)\sim \mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the
initial data and for exponential nonlinearity $f$ such that $f(u)\sim u^m$ as
$u\to 0,$ $m$ integer and $N(m-1)/4\geq 2$, we show that the solution is
global. Moreover, we obtain a decay estimates for large time for the nonlinear
biharmonic heat equation as well as for the nonlinear heat equation. Our
results extend to the nonlinear polyharmonic heat equation.
