Thunderbolt 3 to Thunderbolt 2 adapters only pass Thunderbolt signals (PCIe and DisplayPort streams). Therefore a Thunderbolt device on the other end is required to convert it back to DisplayPort.
Many DisplayPort to HDMI adapters do not support HDMI 2.0. If the product description doesn't say HDMI 2.0 or 4K 60 Hz, then ignore it (even if it does support 4K 60 Hz, you should ignore the product if the manufacturer can't properly describe the specifications).
club-3d and plugable.com have DisplayPort to HDMI 2.0 adapters.
You may need to also buy a mini DisplayPort (male) to DisplayPort (female) adapter, if the HDMI adapter uses a DisplayPort (male) connector.