  We have investigated the correlation between the "paramagnetic" peculiarity
of the normal-to-superconductive phase transition - detected first in a LTSC
tin, in 1989, and then confirmed in HTSC materials with much more higher
resolution (by a sensitive SFCO method) - and the other weakly expressed
effect, detected also both in LTSC & HTSC materials before their heat
capacity's known "jump". In a low-Tc superconductive tin this thermal effect is
detected a half century ago, by Corak, but passed unnoticed so far. We show in
this work that, externally similar these 2 fine effects really and truly have
the same physical roots. To prove this assumption theoretically, and to reveal
the reasons for their common origin, we use here a concept, which admits
existence of two types of the Cooper pairs in SC materials - "singlet" and
"triplet". As we conclude in this paper, they show completely different,
non-traditional temperature behavior upon cooling of SC materials. We believe
that this study results (along with the "triplet" superconductivity, proven
experimentally in Josephson junctions quite recently, with the ferromagnetic
barrier) may obtain key importance for the true understanding of the real
nature of the superconductive phenomenon (in whole) and to uncover electron
"pairing" mechanisms above the Meissner expel (in particular).
