Let's start with the naming of symbols. To keep the hierarchy information from the model intact in the equations in Mathematica, a few special symbols are used:
- "up pointer" that looks like a small triangle, which replaces the "." notation in Modelica
- "underbracket" that looks similar to an underscore, which replaces the "_" in Modelica symbol names
There are a few ways to get a more condensed set of equations.
The most obvious one is to insert the numerical values of all parameters:
eqs = WSMModelData["temp_B_1", "SystemEquations", t];
pars = WSMModelData["temp_B_1", "ParameterValues"];
neqs = eqs //. pars
Which will eliminate all the parameters:

You can simplify knowing that the time variable will be larger than 0:
neqs2 = FullSimplify[neqs, t >= 0]

To do further processing we have to filter out the equations handling events:
{events, otherEqs} = {Select[neqs2, ! FreeQ[#, WhenEvent | If] &],
Select[neqs2, FreeQ[#, WhenEvent | If] &]}
Then we can run Eliminate
to eliminate variables we are not interested in. Here is an example where I have chosen to eliminate some internal variables from the equation system:
sotherEqs =
Eliminate[
otherEqs, {m2\[UpPointer]flange\[UnderBracket]b\[UpPointer]s[t],
m1\[UpPointer]flange\[UnderBracket]a\[UpPointer]s[t],
m1\[UpPointer]flange\[UnderBracket]b\[UpPointer]f[t],
m2\[UpPointer]flange\[UnderBracket]a\[UpPointer]s[t],
k1\[UpPointer]s\[UnderBracket]rel[t]}]

To make things more easily readable, it may help to show equations in a column:
List @@ sotherEqs // Column

Please note the warning that you received on the first evaluation of WSMModelData about algorithms. In this case, there is an initial algorithm
in the pulse component that is not represented in the equations in Mathematica.