The amount of heat given off in a circuit with a given resistance is proportional to the average value for the square of the current strength in the circuit. The readings of the hot-wire ammeter are also proportional to this average value (regardless of the kind of current). Therefore if the ammeter reads 5 amp in both cases, then the heating effect will be the same in both cases also.
But an ammeter with permanent magnets (an electromagnetic ammeter) gives readings which are proportional to the average value for the current. It will show deflections, and in the case of pulsating current it will also show the average value of this pulsating current. But the average value of the square of a pulsating current is not equal to the square of the average value of this current. Therefore if an electromagnetic ammeter gives the same readings for direct and for pulsating current, the heating of the furnace will not be the same in the two cases.