Your online research is correct. Napalm relies on oxygen in the atmosphere in order to burn, so it produces just an ordinary flame.
Ordinary flames reach equilibrium at less than few thousand degrees as radiation and convection carry away the limited energy output available from oxygen travelling towards the fuel.
Note that theA traditional flame is an "oxidation" process which releases energy comes from the breaking of theby replacing oxygen double bondbonds with lower energy bonds. When the fuel is a hydrocarbon, as it is with napalm, the bonding energies of the hydrogen and carbon atoms are about the same as before combustion. Thus, only as oxygen makes its way tois available only from the flame can energy be releasedatmosphere. While While the fuel is concentrated in a solid/liquid state, the gaseous oxygen in the atmosphere takes it time to get to the napalm. This is a major factor limiting the temperature of flames.