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 the energy comes from the breaking of the oxygen double bond. 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 to the flame can energy be released. 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.