Reading odd parts, all warm to mission (5)
I believe the answer is:
alamo
'mission' is the definition.
(famous mission and siege from the Texas revolution)
'reading odd parts all warm to' is the wordplay.
'reading odd parts' means one should take alternating letters (odd letters).
'all'+'warm'+'to'='allwarmto'
The alternating letters of 'allwarmto' are 'ALAMO'.
(Other definitions for alamo that I've seen before include "Famous battle in Texas and John Wayne film" , "Famous Texan fortress" , "US mission" , "historical Franciscan mission" , "1836 massacre at a San Antonio, Texas mission" .)