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

Stochastic Pairwise Alignments, U. Mueckstein, I. L. Hofacker, and P. F. Stadler, Bioinformatics 18 (suppl) 2002.

P. Clote and J. Straubhaar,
Symmetric time warping, Boltzmann pair probabilities and functional genomics, J Math Biol. 53(1):135-61 (2006).

This involves a computation of the forward partition function Z(i,j,T) defined to be the sum of

exp(- sim( [a₁, a_i], [b₁, b_j])/ RT

where the sum is taken over all alignments of the query prefix a₁, ..., a_i, with the target prefix b₁, ..., b_j. 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[a_i,b_j] at high temperature is essentially the number of times a_i is aligned above b_j divided by the number of alignments. Good choice of temperature depends on sequence lengths.