  The quiet solar corona emits meter-wave thermal bremsstrahlung. Coronal radio
emission can only propagate above that radius, $R_\omega$, where the local
plasma frequency eqals the observing frequency. The radio interferometer LOw
Frequency ARray (LOFAR) observes in its low band (10 -- 90 MHz) solar radio
emission originating from the middle and upper corona. We present the first
solar aperture synthesis imaging observations in the low band of LOFAR in 12
frequencies each separated by 5 MHz. From each of these radio maps we infer
$R_\omega$, and a scale height temperature, $T$. These results can be combined
into coronal density and temperature profiles. We derived radial intensity
profiles from the radio images. We focus on polar directions with simpler,
radial magnetic field structure. Intensity profiles were modeled by ray-tracing
simulations, following wave paths through the refractive solar corona, and
including free-free emission and absorption. We fitted model profiles to
observations with $R_\omega$ and $T$ as fitting parameters. In the low corona,
$R_\omega < 1.5$ solar radii, we find high scale height temperatures up to
2.2e6 K, much more than the brightness temperatures usually found there. But if
all $R_\omega$ values are combined into a density profile, this profile can be
fitted by a hydrostatic model with the same temperature, thereby confirming
this with two independent methods. The density profile deviates from the
hydrostatic model above 1.5 solar radii, indicating the transition into the
solar wind. These results demonstrate what information can be gleaned from
solar low-frequency radio images. The scale height temperatures we find are not
only higher than brightness temperatures, but also than temperatures derived
from coronograph or EUV data. Future observations will provide continuous
frequency coverage, eliminating the need for local hydrostatic density models.
