Aside from swelling, can a symptom of an edema of the leg be a thaw out sensation of the member when touched?

Answers:

Usually in edema from hypertension / hypoprotienemia / congestive heart failure, the limb feel colder to the touch.
When the limb feels warmer to the touch you regard as of inflammation and infection as the cause of the swelling (including thrombophlebitis)
Old Doc

Well, swelling is just swelling. A symptom of a DVT can, indeed, be warmth.