Simple analytical models have been derived for the first time, describing the 2-D distribution (along and across the Earth's magnetotail) of the central plasma sheet (CPS) ion temperature, density, and pressure, as functions of the incoming solar wind and interplanetary magnetic field (IMF) parameters, at distances between 10 and 50 RE. The models are based on a large set of data of the Low-Energy Particle (LEP) and Magnetic Field (MGF) instruments, taken by Geotail spacecraft between 1994 and 1998, comprising 7234 1-min average values of the CPS temperature and density. Concurrent solar wind and IMF data were provided by the Wind and IMP 8 spacecraft. The accuracy of the models was gauged by the correlation coefficient (c.c.) R between the observed and predicted values of a parameter. The CPS ion density N is controlled mostly by the solar wind proton density and by the northward component of the IMF. Being the least stable characteristic of the CPS, it yielded the lowest c.c. RN = 0.57. The CPS temperature T, controlled mainly by the solar wind speed V and the IMF Bz, gave a higher c.c. RT = 0.71. The CPS ion pressure P was best controlled by the solar wind ram pressure Psw and by an IMF-related parameter F = B⊥$sqrt{sin left(theta / 2right)}$, where B⊥ is the perpendicular component of the IMF and θ is its clock angle. In a striking contrast with N and T, the model pressure P revealed a very high c.c. with the data, RP = 0.95, an apparent consequence of the force balance between the CPS and the tail lobe magnetic field. No significant dawn-dusk asymmetry of the CPS was found beyond the distance 10 RE, in line with the observed symmetry of the tail lobe magnetic field. The plasma density N is lowest at midnight and increases toward the tail's flanks. Larger (smaller) solar wind ion densities and northward (southward) IMF Bz result in larger (smaller) N in the CPS. In contrast to the density N, the temperature T peaks at the midnight meridian and falls off toward the dawn/dusk flanks. Faster (slower) solar wind flow and southward (northward) IMF Bz result in a hotter (cooler) CPS. The CPS ion pressure P is essentially a function of only XGSM in the midtail (20--50 RE); at closer distances the isobars gradually bend to approximately follow the contours of constant geomagnetic field strength. For northward IMF conditions combined with a slow solar wind, the isobars remain quasi-circular up to larger distances, reflecting a weaker tail current and, hence, more dipole-like magnetic field.