Hello Natalia:  If a drug increases the Tm, then it is either stabilizing the gel phase or destabilizing the fluid phase.  If a drug decreases the Tm, then it is either destabilizing the gel phase or stabilizing the fluid phase.  This is one way to think about it.

Dr. Tristram-Nagle

Hello Natalia:  If a drug increases the Tm, then it is either stabilizing the gel phase or destabilizing the fluid phase.  If a drug decreases the Tm, then it is either destabilizing the gel phase or stabilizing the fluid phase.  This is one way to think about it.

Dr. Tristram-Nagle

What a nice comment from Stephanie :-)... I hardly could add something else...

A drug that partially inserts in the membrane will create a void beneath it causing increased disorder in the lipid tails in this region. This will tend to shift the Tm to lower temperatures (since the ordered gel phase becomes less favorable) and decrease the enthalpy of the transition (since the gel phase becomes more similar to the disordered fluid liquid crystalline phase).

This effect is maximal when the drug is inserted to around the headgroup/glycerol region. When insertion is deeper, the void is smaller and the effect becomes less. The chain disorder can be detected directly by deuterium NMR or by 13C/1H dipolar couplings in bicelles using solid state NMR.An example can be seen here https://www.researchgate.net/publication/24172897_Determining_the_effects_of_lipophilic_drugs_on_membrane_structure_by_solid-state_NMR_spectroscopy_the_case_of_the_antioxidant_curcumin

If the drug makes salt bridges or hydrogen bonds only to the headgroups without inserting, Tm usually increases as this tends to condense the bilayer favoring the gel phase.  

Article Determining the Effects of Lipophilic Drugs on Membrane Stru...

You should  take into account more factors. As an example, for different drug concentrations:

increase of deltaH and Tm: electrostatic surface interaction

decrease of deltaH and Tm: electrostatic surface interactionand partial insertion into the membrane

 linear decrease of deltaH, no changes in Tm: insertion into the membrane

Answering directly to your question - it depends on the specific question. The answer mayl be different if you are looking on lipid bilayer permeability or functioning of membrane (especially transmembrane or membrane associated) proteins (e.g. channels, receptors, enzymes). Most of them require a proper "membrane fluidity" for their functioning. Modern biomembrane models (extending clasical fluid mosaic by Singer and Nicolson) indicate direct and indirect interplay between lipids and proteins (and vice versa). They also include the role of "boundary lipids" and relatively recently indicated role of "rafts". Taking together, it is not so easy to predict or conclude the effects of any xenobiotic (particularly drug) on functioning of the membrane as whole structure. It also should be taken into consideration that drugs entering bilayer will affect not only bilayer lipids properties ("fluidity") but also will directly and indirectly affect properties of proteins. So the effect of any drugs should be considered holistically. Each alteration of the membrane status quo will be reflected in membrane fuction as well as further biological processes e.g. signal transduction. Therefore there is no simple answer of the type YES or NO or FRIEND of FOE.

Thanks a lot to everyone for valuable discussion. 

After your comments I specify my question in such manner:

Is there a correlation between changes in model lipid membrane melting temperature and membrane permeability (or ''fluidity'') upon a drug action?

The answer is yes. In general, the highest permeability is at the region of Tm. The more rigid bilayer is the lower permeability. More fluid is more permeable. Therefore in many pharmacetical formulations a cholesterol is present. It acts as unifier of fluidity. Therefore decrease of fluidity of fluid state and increase of fluidity of rigid state is observed. On the other hand the extent of bilayer permeability depends on the size and nature of the solute. Small hydrophilic drugs permeate faster than large. Solutes as big as large as polyteptides or proteins practically do not permeate. Ionic drugs and other solutes penetrate very slowly therefore loading of amphipatic drugs (the remote loading technique) rely on penetration of bilayer in the nonionized state and undergo ionization inside liposomal environment.. This is similar to glucose transport. Glucose can be transported through biomembrane (facilitated transport) both ways (In and Out). But as it will be phosphorylated (hexokinase) it will become ionic therefore at this state it will not leave the cell the same way as it entered.