Hello Asj,
pulsating DC can be thoought of as DC with overlaid AC. Since the transformer is unable to transfer the DC part of the signal from its primary coil to the secondary, the DC part will only heat the transformer.
You could block the DC by adding a series capacitor to the primary coil. Thus only the AC component of the signal is seen by the transformer. The size of the capacitor depends on factors like frequency of the signal, inductance of the transformer coil, power to be transmitted etc.
Regards,
Harald