  A holographic computation of $T_c$ at ${\it intermediate\ coupling}$ from
M-theory dual of thermal QCD-like theories, has been missing in the literature.
Filling this gap, we demonstrate a novel UV-IR mixing, (conjecture and provide
evidence for) a non-renormalization beyond 1 loop of ${\bf M}-{\bf c}$hiral
perturbation theory arXiv:2011.04660[hep-th]-compatible deconfinement ${\bf
T}$emperature, and show equivalence with an ${\bf E}$ntanglement (as well as
Wald) entropy arXiv:0709.2140[hep-th] computation, up to terms ${\bf Q}$uartic
in curvature. We demonstrate a ${\bf F}$lavor-${\bf M}$emory (FM) effect in the
M-theory uplifts of the gravity duals, wherein the no-braner M-theory uplift
retains the "memory" of the flavor D7-branes of the parent type IIB dual in the
sense that a specific combination of the aforementioned quartic corrections to
the metric components precisely along the compact part of the non-compact
four-cycle "wrapped" by the flavor D7-branes, is what determines, e.g., the
Einstein-Hilbert action at O$(R^4)$. The same linear combination of O$(R^4)$
metric corrections, upon matching the phenomenological value of the coupling
constant of one of the SU(3) NLO ChPT Lagrangian, is required to have a
definite sign. Interestingly, in the decompactification limit of the spatial
circle, we ${\it derive}$ this, and obtain the values of the relevant O$(R^4)$
metric corrections. Further, equivalence with Wald entropy for the black hole
at ${\cal O}(R^4)$ imposes a linear constraint on the same linear combination
of metric corrections. Remarkably, when evaluating $T_c$ from an entanglement
entropy computation in the thermal gravity dual, due to a delicate cancelation
between the ${\cal O}(R^4)$ corrections from a subset of the abovementioned
metric components, one sees that there are no corrections to $T_c$ at quartic
order supporting the conjecture referred to above.
