One idea sits under all of these: something hard gives way. Ice thaws, a frozen dispute melts into a compromise, an opaque text gives up its meaning. The same three letters move from the physical (warming something stiff) to the social (reconciling two sides) to the mental (decoding a sense). Notice how lukewarm, compromise and meaning are not three random words but three faces of one thing softening. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Two binyanim do the work here, and they split the meaning cleanly: pi'el takes the social-mental sense (smoothing people over), hif'il takes the physical one (warming ice). The pa'al, nif'al and the passive moulds are not lexicalized for this root in modern Hebrew, so you will not meet them as everyday verbs.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.