NGC 2024 is a star-forming region in Orion B that contains a dense molecular ridge. A number of dense cores are seen by their dust emission. This area is investigated using observations of four formaldehyde transitions–namely, 303 ⟶ 202, 322 ⟶ 221, 505 ⟶ 404, and 523 ⟶ 422. Maps of the ridge are used to provide temperatures and densities, with a focus on the dense-core positions. The formaldehyde transition ratios 303 ⟶ 202/322 ⟶ 221 and 505 ⟶ 404/523 ⟶ 422 offer measurements of the kinetic temperature, while the ratio 303 ⟶ 202/505 ⟶ 404 allows the evaluation of number densities. The resulting temperatures are very warm (45-85 K), with no observed variation between the core centers and their envelopes. H2 CO number densities of ∼2x106 cm–3 at far-infrared (FIR) core positions and H2 CO column densities in the range of 6x1014 to 1x1015 cm–2 are derived. Using the derived properties in combination with previous submillimeter continuum data, core masses of ∼2 M☉ are found within a 15'' beam size. H2CO fractional abundances are calculated and resemble previous values found in similar star-forming regions–between 2x10–9 and 5x10–9. The virial theorem applied to FIR cores 3, 4, 5, and 6 suggests that all four cores are unstable against gravitational collapse.