  We consider the space of all causal bulk materials, 2D materials, and
metamaterials for maximum near-field radiative heat transfer (RHT). Causality
constrains the bandwidth over which plasmonic response can occur, explaining
two key traits in ideal materials: small background permittivities (minimal
high-energy transitions in 2D materials), and Drude-like free-carrier response,
which together optimally yield 10X enhancements beyond the theoretical
state-of-the-art. We identify transparent conducting oxides, III-Nitrides, and
graphene as materials that should offer nearly ideal near-field RHT rates, if
doped to exhibit plasmonic resonances at what we term "near-field Wien
frequencies." Deep-subwavelength patterning can provide marginal further gains,
at the expense of extremely small feature sizes. Optimal materials have
moderate loss rates and plasmonic response at 19 {\mu}m for 300K temperature,
suggesting a new opportunity for plasmonics at mid- to far-infrared
wavelengths, with low carrier concentrations and no requirement to minimize
loss.
