How do I calculate the proportion of respective conjugates of one base mixed with several acids (and/or conversely) at different temperatures?
If you want a general solution for complex mixtures, where simplified formulas do not apply, you may need to involve numerical mathematics.

As solving the equation set may lead to polynomial equation of higher order you may like.

Enumerate equations of the known.

First, charge balance.
Then, mass balances.
Finally, dissociation equilibriums.

Involve a function of [H+] with a minimum at the value being searched for.

About temperature, there is problem the  constants are rarely provided for other but the standard temperature $\pu{25 ^{\circ}C}$