No, do not put a wig in a clothes dryer unless the manufacturer somehow says it is safe. For most wigs, the dryer is too hot and too rough.
Why dryers are risky
Synthetic fiber can frizz, kink, or melt. Human hair wigs can dry out, tangle, shed, or lose styling. Tumbling also stresses lace, knots, and wefts.
Better drying method
Blot with a towel, place the wig on a stand, reshape the part, and let it air dry away from direct heat.
Bottom line
A wig should air dry. The dryer may save an hour and cost you the whole wig.