How do I get the Redshift functionality of smart adjustment of the color temperature throughout the day in a Wayland session of Ubuntu 17.10?

Not really a good one but kinda half-baked solution is using a GNOME shell extension called "Night Light Slider". It adds a slider to control the colour temperature manually:

(screenshot source: extension's homepage at extensions.gnome.org)

Also you may change Night Light's colour temperature using dconf Editor/gsettings as suggested here: How to adjust the hue (intencity) of gnome night light?

TLDR;

Just for the quick reader who didn't read the whole OP question:

Here is a screenshot of the Solution Ubuntu offers since 17.10, the built-in feature like redshift called "Night Light":

The Night Light feature is extremely easy to enable. We just need to open Settings, and then go to Devices → Display. Here we need to move the button next to Night Light to the “on” position.

Source: https://pentruprieteni.com/en/how-to/how-to-enable-night-light-on-ubuntu-17-10/