#Haskell, 84 bytes

import Data.List
p(t:'h':'e':' ':s)|elem t"Tt"=s
p s=s
sortBy(\a b->p a`compare`p b)

Call with

sortBy(\a b->p a`compare`p b)["The The", "The They", "Thermodynamics"]

Testcase:

let s = sortBy(\a b->p a`compare`p b)
and[s["Queen", "Aerosmith", "Sunny Day Real Estate", "The Strokes"]==["Aerosmith", "Queen", "The Strokes", "Sunny Day Real Estate"],s["The Ramones", "The Cure", "The Pixies", "The Roots", "The Animals", "Enrique Iglesias"]==["The Animals", "The Cure", "Enrique Iglesias", "The Pixies", "The Ramones", "The Roots"],s["The The", "The They", "Thermodynamics"]==["The The", "Thermodynamics", "The They"]]

Haskell, 84 bytes

import Data.List
p(t:'h':'e':' ':s)|elem t"Tt"=s
p s=s
sortBy(\a b->p a`compare`p b)

Call with

sortBy(\a b->p a`compare`p b)["The The", "The They", "Thermodynamics"]

Testcase:

let s = sortBy(\a b->p a`compare`p b)
and[s["Queen", "Aerosmith", "Sunny Day Real Estate", "The Strokes"]==["Aerosmith", "Queen", "The Strokes", "Sunny Day Real Estate"],s["The Ramones", "The Cure", "The Pixies", "The Roots", "The Animals", "Enrique Iglesias"]==["The Animals", "The Cure", "Enrique Iglesias", "The Pixies", "The Ramones", "The Roots"],s["The The", "The They", "Thermodynamics"]==["The The", "Thermodynamics", "The They"]]