I am interested in the chemical differences shown in a pvc cable
sheath that has been melted. Can you tell from a sprectrograph or
similar if the melting was caused by say a blow torch or the cable
sheath being in contact with a hot metal object, what if any would be
the differencews in the chemical composition of the melted pvc or the
burn pattern?

This question does not have a yes or no answer:

Unlike the low molecular weight materials, polymers do have memory,

they remember the thermal and mechanical history.

For how long they remember, that is a very complex question.
Here is basic info on such properties of polymers:

http://dmoz.org/Science/Physics/Rheology/

For 'typical' PVC in melted phase memory would be on order of minutes.

Melt has same chemical composition as solid, by definition.

If you stir the melt well, you destroy any memory.

On the other hand, if you have a sample of original PVC before melting,
and one method of heating exposed the material to higher temperatures
than the other method, you will see some differences due to degradation:

http://www.specialchem4polymers.com/tc/Tin-Stabilizers/index.aspx?id=2821
http://www.nohsc.gov.au/OHSInformation/NOHSCPublications/fulltext/docs/h4/601.htm

Degradation means that polymer chains break (in half), and that lowers
the molecular weight.

The simple way to test it would to determine that would be  measure
visocsity of the melt. Instruments look like this:

http://images.google.com/images?svnum=10&hl=en&safe=off&q=+melt+viscometer&spell=1

and are not dificult to use.

What you determine is an indirect indication of the thermal history,
mainly the peak temperature and that may differentiate between the blow torch
and contact with the hot metal.

Hedgie

Many thanks for the useful information