  The frequency stability of lasers is limited by thermal noise in
state-of-the-art frequency references. Further improvement requires operation
at cryogenic temperature. In this context, we investigate a fiber-based ring
resonator. Our system exhibits a first-order temperature-insensitive point
around $3.55$ K, much lower than that of crystalline silicon. The observed low
sensitivity with respect to vibrations ($<5\cdot{10^{-11}}\,\text{m}^{-1}
\text{s}^{2}$), temperature ($-22(1)\cdot{10^{-9}}\,\text{K}^{-2}$) and
pressure changes ($4.2(2)\cdot{10^{-11}}\,\text{mbar}^{-2}$) makes our approach
promising for future precision experiments.
