We present estimates of volume and heat transport through Fram Strait for the period 1997 to 2000 from data of moored instruments. The annual mean volume transports at 78¿55'N were between 9 $mp$ 2 and 10 $mp$ 1 Sv northward and 13 $mp$ 2 and 12 $mp$ 1 Sv southward with a net transport between 4 $mp$ 2 and 2 $mp$ 2 Sv to the south. The temperature of the northward flow of Atlantic Water had a strong seasonality with a minimum in winter. Nevertheless, the northward heat transport was highest in winter caused by the winter maximum of northward volume transport. Between 1997 and 1999, the annual mean net heat transport across 78¿55'N increased from 16 $mp$ 12 to 41 $mp$ 5 TW. This resulted from a very strong increase in heat transport in the West Spitsbergen Current (mean annual values from 28 $mp$ 5 to 44 $mp$ 6 TW and to 46 $mp$ 5 TW in 99/00) which was not compensated by an equivalent signal in the southward flow. The heat transport to the south remained constant within error limitations. Only half of the heat flux increase in the West Spitsbergen Current was due to a higher temperature; half of it was due to a stronger flow. A similar increase as observed between 1997 and 2000 would have been sufficient to explain the warming of intermediate layers in the Eurasian Arctic observed in the early 1990s. Consequently, we suggest that a warming signal from the late 1990s is presently spreading in the interior Arctic Ocean.