Many materials especially biological origin shows the transition only during heating like protein denaturation, starch gelatinization etc. But crystalline or semicrystalline polymeric materials exhibit glass transition which you can observe both during heating and cooling whereas melting is observed during heating and crystallization curve during cooling.

the answer is easy. Yes.

Many structural transition are irreversible. In this case you can see signal only in first heating.

Dear macro Signorelli, can u please upload any reference.thanks in adavnce

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2977967/

http://www.ncbi.nlm.nih.gov/pubmed/9218168

Prerna P. Dhawade٭ and Ramanand N. Jagtap "Characterization of the glass transition temperature of chitosan and its

oligomers by temperature modulated differential scanning calorimetry"  Advances in Applied Science Research, 2012, 3 (3):1372-1382.

Galina G. Zhadan ~, Cesar Cobaleda, Ahmik L. Jones z, Fernando Leal, Enrique Villar

and Valery L. Shnyrov I "PROTEIN INVOLVEMENT IN THERMALLY INDUCED STRUCTURAL

TRANSITIONS OF PIG ERYTHROCYTE GHOSTS" BIOCHEMISTRY and MOLECULAR BIOLOGY INTERNATIONAL Vol. 42, No. 1, June 1997 Pages 11-20

Wajira S. Ratnayake, Chika Otani, David S. Jackson "DSC enthalpic transitions during starch gelatinization in excess water, dilute sodium chloride, and dilute sucrose solutions"  University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln.  5-15-2012

You can search in google your specifics materials.