Boltzmann pair probabilities can be computed as explained in the following papers.

This involves a computation of the forward partition function Z(i,j,T) defined to be the sum of
exp(- sim( [a1, ai], [b1, bj])/ RT
where the sum is taken over all alignments of the query prefix a1, ..., ai, with the target prefix b1, ..., bj. Unlike the case of RNA, temperature plays only a formal role, and as show in Clote-Straubhaar, by overlaying the pair probabilities computed at different temperatures, one can see highly significant regions within an optimal alignment.

Boltzmann partition function computation is EXPENSIVE, hence the default is not to do this computation.

Default temperature values are indicated in the web form. Temperature is purely a formal variable, having no physical meaning in the alignment. Since high temperatures weigh all alignments approximately equally, the Boltzmann pair probability Pr[ai,bj] at high temperature is essentially the number of times ai is aligned above bj divided by the number of alignments. Good choice of temperature depends on sequence lengths.