Both kinds of molecules should have the same speed.
In most matter, the molecules have a energy called kinetic energy. Kinetic energy is about the speed of movement of the molecules. Kinetic energy is also the temperature of the object, which means, if the temperature of the object is higher, the kinetic energy of the molecules is higher too.
Therefore, when 2 objects have the same temperature, their molecules that makes up of them has the same kinetic energy, and this also explains why the speed of them is the same too.
