  The late-type dwarf GJ 436 is known to host a transiting Neptune-mass planet
in a 2.6-day orbit. We present results of our interferometric measurements to
directly determine the stellar diameter ($R_{\star} = 0.455 \pm 0.018
R_{\odot}$) and effective temperature ($T_{\rm EFF} = 3416 \pm 54$ K). We
combine our stellar parameters with literature time-series data, which allows
us to calculate physical and orbital system parameters, including GJ 436's
stellar mass ($M_{\star} = 0.507^{+ 0.071}_{- 0.062} M_{\odot}$) and density
($\rho_* = 5.37^{+ 0.30}_{- 0.27} \rho_\odot$), planetary radius ($R_{p} =
0.369^{+ 0.015}_{- 0.015} R_{Jupiter}$), planetary mass ($M_{p} = 0.078^{+
0.007}_{- 0.008} M_{Jupiter}$), implying a mean planetary density of $\rho_{p}
= 1.55^{+ 0.12}_{- 0.10} \rho_{Jupiter}$. These values are generally in good
agreement with previous literature estimates based on assumed stellar mass and
photometric light curve fitting. Finally, we examine the expected phase curves
of the hot Neptune GJ 436b, based on various assumptions concerning the
efficiency of energy redistribution in the planetary atmosphere, and find that
it could be constrained with {\it Spitzer} monitoring observations.
