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 436s 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.
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