  We study the intrinsic transport properties of suspended graphene devices at
high fields (>1 V/um) and high temperatures (>1000 K). Across 15 samples, we
find peak (average) saturation velocity of 3.6x10^7 cm/s (1.7x10^7 cm/s), and
peak (average) thermal conductivity of 530 W/m/K (310 W/m/K), at 1000 K. The
saturation velocity is 2-4 times and the thermal conductivity 10-17 times
greater than in silicon at such elevated temperatures. However, the thermal
conductivity shows a steeper decrease at high temperature than in graphite,
consistent with stronger effects of second-order three-phonon scattering. Our
analysis of sample-to-sample variation suggests the behavior of "cleaner"
devices most closely approaches the intrinsic high-field properties of
graphene. This study reveals key features of charge and heat flow in graphene
up to device breakdown at ~2230 K in vacuum, highlighting remaining unknowns
under extreme operating conditions.
