"maybe it is actually Titan's inhabitants desperately moving their moon closer to sun to warm up ?"
As Titan is in orbit around Saturn, it is highy unlikely that Titan would be moving closer to the Sun.
Titan might get 11 cm closer to the Sun (each year) IF apogee AND Titan eclipsing Saturn occured at the same time.
And when Saturn eclipses Titan, Titan would of course be getting FURTHER away from the Sun, by a whole 11 cm.
(One assumes it is the mean radius of Titans orbit that is increasing at 11 cm per year).