  The puzzling situation where some thermodynamic quantities require a
single-gap description, while others need a more complex gap scenario, is
discussed. Our approach reveals that in some cases, the conclusions based on
measurements of only one thermodynamic quantity may lead to conflicting
results. As an example, temperature evolutions of the electronic specific heat
[$C_{\rm e}(T)$] and the thermodynamic critical field [$B_{\rm c}(T)$] of BeAu
superconductor were reconsidered within the framework of the single-gap and the
two-gap scenarios. The analysis shows that the single-gap approach describes
the temperature dependencies of $C_{\rm e}(T)$ and the superfluid density
$\rho_{\rm s}(T)$ satisfactorily. However it fails in the case of $B_{\rm
c}(T)$. The self-consistent two-gap model, in contrast, is able to describe all
of the mentioned thermodynamic quantities by using a similar set of parameters.
Our results reveal that a proper description of the thermodynamic quantities,
related to the superconducting pairing mechanism, requires the use of similar
model containing the same set of parameters.
