The right temperature for lead-free soldering?

Unleaded solder generally does require higher temps. From the datasheet you linked:

Lead free/leaded solder comparison Lead Free Solder (Sn/Ag/Cu) Sn63/Pb37 (Leaded Solder)
Melting Point 217-221 º C (422.6 - 429.8 º F) 183 º C (361.4 º F)