What he means is: The sun IS the source of the world’s 9average) climate. As it increases (net radiation + cosmic ray shielding) temperatures rise above their nominal. When the sun’s activity decreases, temperatures on earth cool (go down) from their nominal point.
Over the very long term, the sun either heats things up (1908-1935, 1970-1998) or cools things off (Maunder Minimum/Little Ice Age, 1940-1970, 2007-2008).
Decreased insolation leading to a relative change from a nominal point is "allowing it to cool"--not "cooling it"--which is perhaps why he's so off-base with this statement: "Curiously, the Sun never has been seen as a cooling agent [...]" Of course it hasn't--since it isn't!
It’s not like William Stanley Jevons wouldn’t show up in a good literature search, either.