What is the most efficient way to use a blow torch? Let's start with a torch and a piece of titanium.  What is the fastest way to get the titanium up to red hot?  I am not going for getting the Titanium malleable, just red hot.

Whenever I ask my science-y friends they like to point out that the bright blue tip is the hottest point in the torch flame.

But this doesn't take into account heat transfer.  Aren't we better off with having more flame spread out on the metal transferring heat over a larger area even if that flame isn't at the most extreme possible temperature?  What is the optimum balance between heat transfer area and temperature?
 A: That's not an easy one...
First of all you must know the final temperature you are trying to achieve, then you need to choose a heat source and a way to trap heat where you need it
I'd sugest you build a "soup-can forge" or something like that and use a MAP-gas torch.
A J23 ceramic hoven brick might also be a good choice, maybe even easier to make.
With that setup I manage to get steel to about 800°C to heat treat small knives I make.
A: Heat is the total energy of molecular motion in a substance while temperature is a measure of the average energy of molecular motion in a substance.1
To heat up something faster, you need more heat. This could mean a higher temperature, or more heated molecules (more substance/surface area). The usage cases differ, but if the surface area is relatively small compared to the proportion of temperature you can change, you'd probably be better off using the higher temperature as blow torches can vary widely in temperature between the different flames.
A: For some jobs you need a 'softer' flame, or a reducing or oxidising flame. The hottest part of the flame is not always the best flame for the job.
A: You can use the hottest part of the flame, the tip, to heat your titanium nail, but you don't need it red hot for what you are doing. Get a laser thermometer and figure out the optimal temp for your distillate, figure out the most efficient temp to get it to in order to have it be at optimal temperature the second the distillate hits it. Terpenes are volatile. Don't want to destroy them. 
A: Blue flame is an indicator of complete combustion which is more efficient.  But that is not taking into consideration the type of material, gas, etc is being burned.  For example, Propane torches flame are usually blue with a yellow tip.  My Propane torch flame is blue.  That is because I am using a torch tip that I made myself.  The focal point is the hottest but not always the best choice or the most efficient.  It all depends on what you are trying to accomplish.  There are many other things to consider.  But to answer your question, The fastest to get red hot is to use the focal point.
A: You didn't specify why you want to heat titanium, so I'll guess you want to forge it.  Titanium has a relatively narrow range of temperatures over which it can be forged, and it oxidizes readily.  
In that case, you want to be careful to heat the entire portion of the workpiece to the same temperature, and you want to do it relatively slowly to keep the temperature uniform.  And, you want to use a flame without too much excess oxygen.  So, I recommend using the portion of the flame that is beyond the blue tip of the flame because it will contain a lower ratio of oxygen and because it is spread out more.  Also: a huge amount of heat is lost via radiation (it'sproportional to the fourth power of temperature), so when I'm heating a piece with a torch I usually do it inside a cavity made with firebrick or Kaowool, or even just on top of a firebrick or section of Kaowool, to prevent heat loss off the back side of the workpiece.
