It is well known that there is an up-down difference in temperature intokamaks. In the collisional case this difference for ions is on the order of1/(ωBiτ)>>1 for a circular cross section tokamak, whereωBi and τi are the ion cyclotron frequency and collision time,respectively. Here we show that the presence of an X-point amplifies thiseffect and can lead to effects of order of unity, depending on the ion driftdirection. This in turn leads to a strong increase of the pressure gradient inthe vicinity of the X-point (if the drift of the ions is in the X-pointdirection). In the framework of the Alfvén-drift paradigm for the L-Htransition, it provides an explanation for the difference in the powerthreshold for the L-H transition arising from the ion drift direction.