Passing a function as an argument to another function using the same variables

I define a function with two variables and an argumment which is a function of this two first variables. For example the function Ttrho below (the two variables are T and Rho and pTt is a function of T or Rho or both):

getAllVariables[expr_] := 
Union@Cases[expr, 
Except[__Symbol?(Context@# === 
     "System`" &), _Symbol], {1, ∞}, Heads -> True];

Ttrho[T_, ρ_, pTt_] := 
With[{var = getAllVariables[pTt]}, Print[var]; 
If[Length@var > 0, 

Apply[pTt, var /. Thread[var -> {T, ρ}]] 5 0.069/ρ, 
pTt*5 0.069/ρ]]

I would like that the three results below must have the same value:

Ttrho[1, 0.1, Function[{T, ρ}, T]]
Ttrho[1, 0.1, Function[{ρ, T}, T]]
Ttrho[1, 0.1, Function[T, T]]

But I obtain actually the following results:

During evaluation of In[1]:= {T,ρ}

Out[1]= 3.45

During evaluation of In[2]:= {T,ρ}

Out[2]= 0.345

During evaluation of In[3]:= {T}

During evaluation of In[3]:= Thread::tdlen: Objects of unequal length in {T}->{1,0.1} cannot be combined.

Out[3]= 3.45

Thank you in advance.

Comments

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