shuttle bus from beijing airport to holiday inn temple of heaven and from temple of heaven to tianjin port

No direct bus can take you to reach your hotel directly.
You can take the airport shuttle bus line 10 to reach Yuting Bridge (Yuting Bridge West) and then take a taxi to reach your hotel directly. From Yuting Bridge (Yuting Bridge West) to your hotel, there is about 2km.
For Tianjin Port, do you refer to the one in Tanggu?
If so, from Temple of Heaven, you can take a taxi to reach the local South Railway Station where you can take the intercity trains to reach Tianjin Railway Station. Then take the Tianjin Light Rail to reach Citizen Square. Then take a taxi to reach Tianjin Port.