Differential emission measure tomography (DEMT) and white light (WL) tomography were applied to study the three‐dimensional (3D) structure of the global solar corona for two Whole Heliosphere and Planetary Interactions campaign periods, Carrington rotations 2219 and 2223. With DEMT, Solar Dynamics Observatory/Atmospheric Imaging Assembly images were used to reconstruct the 3D coronal electron density and temperature in the range of heliocentric distance 1.02–1.25 R ⊙ . With WL tomography, Solar and Heliospheric Observatory/Large Angle and Spectrometric COronagraph‐C2 images were used to reconstruct the 3D electron density in the range of heliocentric distance 2.5–6.0 R ⊙ . The two periods were also simulated with the 3D‐magneto‐hydrodynamic Alfvén Wave Solar Model (AWSoM), and its results compared in detail with the reconstructions. The DEMT analysis reveals a 20% less dense and 20% hotter corona than for rotations corresponding to the solar cycle 23/24 deep minimum. The electron density and temperature of the AWSoM model agree with DEMT results within 10% and 20%, respectively, while its electron density overestimates results of WL tomography up to 75%. The slow (fast) component of the terminal wind speed of the model is found to be associated with field lines characterized by larger (smaller) values of the tomographic density and temperature at the coronal base. DEMT reconstructions reveal the coronal plasma to be ubiquitously characterized by temperature variability of up to ≈45% over spatial scales of order ∼10 4 km. Taking into account this level of fine‐structure by global models may be consequential for their predictions on wave propagation in the corona.