I am looking for a manufacturer or distributor who sale 1/8"dia copper thin wall
tubing.Wall thickness may be .003" - .005".

The wall thickness you specified seems absurdly thin, so working on
the assumption that perhaps you put an extra decimal place in your
specifications, there are many companies that manufacture thin walled
copper tubing (again subtracting one decimal place).  These companies
include, but are by no means limited to:

National Copper Products
http://www.nationaltube.com/ncp

From those specifications (minus the decimal place) you would most
likely be able to acquire what you need at any well stocked hardware
store.

The general idea behind a heat exchanger is not that the walls are
spectacularly thin, but that the tubes are thin enough so the liquid
within is cooled.  If I were making a heat exchanger I would opt for
stainless steel instead of copper.  Although it is somewhat more
difficult to put together it will last longer and, if you change
liquids travelling through it, easier to clean.

Enjoy.

You can find everything you require at  www.tubenet.org  or 
www.tubenet.org.uk
If not follow the link to 'Karl Imhauser Gmbh&Co Germany'. They are
the world leaders in thin wall 'Seamless Drawn Tube'. However, it is
very expensive (6 to 10 times the price of 'Fabricated Tube' made from
rolled strip).

I am assuming that your request for thin wall tube means that you wish
to fabricate a 'Compact Heat Exchanger'. Typically,this type of HE
uses very thin material, especially if it is Air/Liquid as in Auto
Radiators. Typically, material thickness is 0.1 mm (0.004")about the
limit for commercial production.
Now, tube diameter of 3mm is very difficult to produce at 0.1 mm,so if
possible you will need to increase to say 6 mm dia. A further
consideration with Air/Liquid HE is the Air Surface Area/Liquid
Surface Area Ratio. This can be in the region of 6 to 14 / 1 if a high
efficiency is required. Equally, the efficiency is also very sensitive
to the material thickness (Thermal Transmissivity).

I have included the last para in case you have the flexibility to
pursue easier fabrication techniques. HE is a very complex subject, so
please feel free to contact me privately for further help if this is
necessary. I should confess to being a retired Consultant in this
field.