@Czarcasm
Okay so I can think of "branching" similar to how I think of cholesterol (in that it prevents the "extremes")
"I'm not entirely sure if it would be reasonable or fair to compare a saturated hydrocarbon and an alkene of similar molecular weights, since the intermolecular interactions would be very similar."
I thought the only "fair" comparisons in organic chemistry were between compounds of roughly the same molecular weight. Otherwise, you'd have to consider molecular weight (which I believe increases both MP and BP)
I'm glad you brought up that distinction. That's only true, particularly when the focus is exclusively on the polarity of molecules/compounds (and their associated intermolecular interactions). For instance, it's only fair to compare a water molecule to an alkane, or any other molecule of similar weight. The testing point here is the strength of intermolecular interactions, given all things equal (in this case, molecular weight). A much larger alkane would have a larger degree of weaker intermolecular interactions that can trump the smaller amount of stronger intermolecular interactions of H2O). This can make the comparison more difficult.
In the scenario you described above, you're comparing molecules with very similar intermolculer interactions - namely, london dispersion forces. In this case, only two things will largely effect the melting and boiling point of the substance: the molecular weight and branching.
It's good that you're trying to relate the concepts together, but I prefer to think of membrane fluidity as mutually exclusive to the independent boiling/melting points of the modulators themselves (ie. cholesterol). Membrane fluidity is largely effected due to temperature. You know from experience, leaving butter on the table will cause it to melt. In the plasma membrane of living organisms, the fatty acids of phospholipids play a role in membrane fluidity (but the fluidity itself is regulated by cholesterol). Unsaturated fatty acids have a kink and promote a more fluid structure, whereas Saturated fatty acids pack more tightly (a more rigid structure). For eukaryotic organisms, changing individual phospholipids to alter fluidity is cumbersome because eukaryotic cells are so large. However, for smaller organisms like bacteria, they can alter these fatty acids to change (ie. from saturated to unsaturated) in a time-appropriate manner due to their smaller size; in addition, they lack the cholesterol .
In some eukaryotic organisms, like humans, cholesterol is the major regulator of membrane fluidity, since this steroid is easily produced by living cells and added to membranes to alter fluidity as needed (in a relatively time-efficient manner). It essentially broadens the spectrum of membrane fluidity: in more hot environments (where membranes become more fluid), it helps phopholipids pack more tightly (less fluid), but in cooler environments (where membrane becomes more rigid), it helps promote fluidity (looser packing). This is why cholesterol is so important for living organisms and their individual cells. When cells become too rigid, they are more prone to mechanical disruption such as lysis, and obtaining essential nutrients become more difficult, if not impossible. Hope this helps.
edit: gosh by typos are horrible