(1) According to the conservation of energy, the process from when the cd edge just enters the magnetic field to when the cd edge just passes through the magnetic field is studied: the kinetic energy becomes zero, and the gravitational potential energy is converted into the heat generated by the wire frame, and q = mgd.

The velocity of cd edge is v0 when it just enters the magnetic field and v0 when it just leaves the magnetic field.

So the heat generated by the wire frame is equal to the heat generated when the cd edge just passes through the magnetic field and the ab edge leaves the magnetic field.

Therefore, when the coil enters the magnetic field from the cd side to the ab side, the heat q ′ = 2 mgd, and the work done by the induced current is 2 mgd.

(2) Because when entering the magnetic field, it is necessary to slow down, that is, the ampere force is greater than gravity at this time, and the speed is reduced, and the ampere force is also reduced. When the ampere force is reduced to equal to gravity, the coil will move at a uniform speed and accelerate when it enters the magnetic field.

Let the minimum speed of the coil be vm. According to the kinetic energy theorem, when the cd edge just enters the magnetic field and the wireframe completely enters, there will be 12mv2m? 12mv20=mgL？ Mgd, and 12mv20 = mgh. To sum up, the minimum speed of the coil is 2g(h+L? d)，

So the answer is: 2mgd, 2g(h+L? d)。