We apply the standard technique of Null Melvin Twist to the non-extremal (D1, D3) bound state configuration of type IIB string theory. Under a particular decoupling limit, such configuration represents the gravity dual of the non-relativistic, non-commutative Yang-Mills theory at a finite temperature. We then use the AdS/CFT and the string probe approach to compute the drag force on an external quark moving through such a hot non-relativistic, non-commutative YM plasma. We discuss various limiting cases to show the interplay between the non-relativistic as well as the non-commutative effect of the general drag force expression.