  A model with d-wave pairing symmetry is studied by employing a
non-perturbative sum rule approach. At low temperature the magnitude of a
normal state pseudogap shows strong $\vec{k}$ or angle dependence well fitted
by $\cos 2\phi$ form. With increasing temperature, the pseudogap closes at some
critical angle $\phi_{c}$ and beyond this angle a single quasiparticle-like
peak appears. The resulting Fermi surface is strongly temperature dependent.
Both in the spectral function and the density of states, the pseudogap
disappears in a manner that the spectral weight fills in the pseudogap instead
of closing it with increasing temperature. All these features are qualitatively
consistent with ARPES for underdoped cuprates.
