No, it is thermoplastic as it can be re-heated and re-shaped.
If it has the recycled number on the bottom (probably code 2 HDPE) it is definately thermoplastic. One characterisitics of thermoplastics is that they can melt and be remoulded whereas thermosetting plastics can not (they will char). Therefore, it logically follows that if it can be recycled it will be a thermoplastic polymer.
Thermosetting
HDPE= High-density polyethylene
thermosetting material
Sometimes
thermosetting plastic
Thermosetting
It is a thermosetting polymer
High Density Polyethylene (HDPE)
the opposite to thermosetting plastic is thermoplastic
thermosetting
LDPE is softest, HDPE is harder, PMMA is much harder than HDPE