  The spin 1/2 Heisenberg model on a square lattice with antiferromagnetic
nearest- and next-nearest neighbour interactions (the $J_1$--$J_2$ model) has
long been studied as a paradigm of a two-dimensional frustrated quantum magnet.
Only very recently, however, have the first experimental realisations of such
systems been synthesized. The newest material, Pb$_2$VO(PO$_4$)$_2$ seems to
have mixed ferro-- and antiferromagnetic exchange couplings. In the light of
this, we extend the semiclassical treatment of the $J_1$--$J_2$ model to
include ferromagnetic interactions, and present an analysis of the finite
temperature properties of the model based on the exact diagonalization of 8, 16
and 20 site clusters. We propose that diffuse neutron scattering can be used to
resolve the ambiguity inherent in determining the ratio and sign of $J_1$ and
$J_2$ from thermodynamic properties alone, and use a finite temperature Lanczos
algorithm to make predictions for the relevant high temperature spin-spin
correlation functions. The possibility of a spin-liquid phase occurring for
ferromagnetic $J_1$ is also briefly discussed.
