In a location that is a warm climate (Austin,Texas), from a cost
economic basis is it more desirable to install double pane thermal
windows or single pane thermal windows (tinted).  During the summer
the temperature diffential between outside air and inside the house is
about 20-25 degrees, in the winter it is about a 30 degree diffential.
 I would like to know how much more energy efficient, if any the
double pane thermal windows are compared to single pane (on a
percentage basis) under the temperature diffentials noted above. In
other words does it cost 40%, 50%, 60% or what % less in electricity
to use dobule pane. I have been told that it is not much of a
advantage in Texas but may be so in areas like Minnesota where in the
winter the diffential is 70-80 degrees between inside and out.

first off, you can not have single pane thermal windows (tinted) all
thermal windows are at least 2 panes.

To answer the other parts of your question, i need to know the glass
make up of what thermal units you are hoping to use.  ie clear on
clear, tinted on clear, low-e on clear, what kind of low-e etc., argon
gas, what kind of spacer bar, and lots of other variables, such as is
the window on a north, south, east or west elevation.

thermal windows pay for themselves (especially with low-e) not only in
the winter, by keeping the heat in, but also in the summer by keeping
the heat out.  If you are considering changing the windows in the
house, go to a reputable window company in your area, and ask them
what is the best for your area. (not a place like home depot) Don't
forget that good advice can save you thousands, so paying a couple
hundred bucks more for the right window, can actaully save you money.

One thing I forgot to add, is it will also add to the re-sale value of your home!

Here is a resource.
http://www.superiormetalproducts.com

Keith
Superior
Wholesale Manufacturers of Quality Vinyl-Aluminum Building Products
Sunrooms - Replacement Windows - Replacement Doors - Carports
Walkway Canopies
http://www.SuperiorMetalProducts.com
http://www.SuperiorSunrooms.com

There's no simple answer to your question. In order to give a solid,
quantitative answer, you would need to do a "load analysis" on your
home. This would take into account the R values and surface areas of
the surfaces of your home - windows, doors, walls, ceiling, floor,
etc.

Also, of particular importance in warm, sunny climates will be the
orientation of the windows. For example, if you have a large area of
south facing windows, you will get a tremendous heat gain from solar
heating effects. A simple and cost effective solution at reducing heat
gain on any sunny window is to use greenhouse shade cloth. This is
installed on the outside of your windows and can reduce the amount of
heat that makes it into your home by up to around 80%. Another option
is to add small awnings outside the south facing windows so that they
are shaded during the summer but let the sun come in during the winter
when it's lower and you want the solar heat gain.

These simple, inexpensive solutions represent the most basic passive
solar design but can yield great benefits to most homes.

For windows that don't get sun (i.e. on the North side of the house),
you'll have to compute what it's worth to you. for example, it a
typical older home construction, you might have your walls at R10 and
your single pane windows at R1. The rough formula for your heat loss
is a simple calculation of area divided by R value times temperature
difference. So, if your north wall has an area of 500 square feet of
which 100 sq. ft. are windows, and it's 40 degrees outside, 70 degrees
inside, then:
Actual wall area = 500 - 100 = 400sq. ft.
wall heat loss = 400 / 10 * (70-40) = 40*30 = 1200 BTU/hour.
Window heat loss = 100 / 1 * 30 = 3000 BTU/hour.
So, you see that your windows will lose 30/12 as much energy as your
walls. If you go to nice, double glazed, low e windows that are R3,
you might get:
loss = 100 / 3 * 30 = 1000 BTU/h
saving you 2000 BTU/h. 
In addition, you have air infiltration losses and gains. If your
current windows are old and you can feel a draft, then you are likely
losing more energy from the draft than you are for the window itself.
Well built new windows will greatly reduce this energy loss and likely
save considerable energy.

Will you ultimately save $ by replacing your windows? Depends on all
these factors and more. If you have to spend $10,000 replacing windows
around your house, that's a lot of utility bills and on a strictly
financial basis, you may not make the money back. However, there are
the intangible effects of upgrading your windows. tight, Low e windows
will make the house feel more comfortable in the winter since your
body heat won't be going out the window. You won't feel the drafts as
much. The temperature in your house will be more even. Your furniture
and carpets won't fade as much due to the sun's damaging UV. You'll be
reducing your energy usage, which these days is a very good thing.

good luck!