  Thin garnet films are becoming central for magnon-spintronics and
spin-orbitronics devices as they show versatile magnetic properties together
with low magnetic losses. These fields would benefit from materials in which
heat does not affect the magnetization dynamics, an effect known as the
non-linear thermal frequency shift. In this study, low damping Bi substituted
Iron garnet (Bi:YIG) ultra-thin films have been grown using Pulsed Laser
Deposition. Through a fine tuning of the growth parameters, the precise control
of the perpendicular magnetic anisotropy allows to achieve a full compensation
of the dipolar magnetic anisotropy. Strikingly, once the growth conditions are
optimized, varying the growth temperature from 405 {\deg}C to 475 {\deg}C as
the only tuning parameter induces the easy-axis to go from out-of-plane to
in-plane. For films that are close to the dipolar compensation, Ferromagnetic
Resonance measurements yield an effective magnetization $\mu _{0}M_{eff} (T)$
that has almost no temperature dependence over a large temperature range (260 K
to 400 K) resulting in an anisotropy temperature exponent of 2. These findings
put Bi:YIG system among the very few materials in which the temperature
dependence of the magnetic anisotropy varies at the same rate than the
saturation magnetization. This interesting behavior is ascribed
phenomenologically to the sizable orbital moment of $Bi^{3+}$.
