The turbulent burning velocity of premixed flames is sensitive to the turbulence intensity of the unburned mixture. Premixed flame propagation models that incorporate these effects of turbulence rest on either of the two hypotheses proposed by Damköhler. The first hypothesis applies to low-intensity turbulence that acts mainly to increase the turbulent burning velocity by increasing the flame surface area. The second hypothesis states that, at sufficiently high intensities of turbulence, the turbulent burning velocity is governed mainly by enhanced diffusivity. Most studies to date have examined the validity of the first hypothesis under increasingly high intensities of turbulence. In the present study, the validity of Damköhler’s second hypothesis is investigated. A range of turbulence intensities is addressed by means of direct numerical simulations spanning the “flamelet” and “broken reaction zones” regimes. The validity of Damköhler’s second hypothesis is found to be strongly linked to the behaviour of turbulent transport within the flame.