  The fundamental rovibrational band of CO near 4.7 $\mu$m is a sensitive
tracer of the presence and location of molecular gas in the planet-forming
region of protoplanetary disks at 0.01--10 AU. We present a new analysis of a
high-resolution spectral survey (R$\,\sim\,$96,000, or $\sim3.2\,\rm
km\,s^{-1}$) of CO rovibrational lines from protoplanetary disks spanning a
wide range of stellar masses and of evolutionary properties. We find that the
CO emission originates in two distinct velocity components. Line widths of both
components correlate strongly with disk inclination, as expected for gas in
Keplerian rotation. By measuring the line flux ratios between vibrational
transitions $F_{v=2-1}/F_{v=1-0}$, we find that the two velocity components are
clearly distinct in excitation. The broad component ($\rm
FWHM=50-200\,km\,s^{-1}$) probes the disk region near the magnetospheric
accretion radius at $\approx0.05$ AU, where the gas is hot ($800-1500$ K). The
narrow component ($\rm FWHM=10-50 km\,s^{-1}$) probes the disk at larger radii
of 0.1--10\,AU, where the gas is typically colder (200--700 K). CO excitation
temperatures and orbital radii define an empirical temperature-radius relation
as a power law with index $-0.3\pm0.1$ between 0.05--3 AU. The broad CO
component, co-spatial with the observed orbital distribution of hot Jupiters,
is rarely detected in transitional and Herbig Ae disks, providing evidence for
an early dissipation of the innermost disk. An inversion in the temperature
profile beyond 3 AU is interpreted as a tracer of a regime dominated by UV
pumping in largely devoid inner disks, and may be a signature of the last stage
before the disk enters the gas-poor debris phase.
