This might help from a 2008 and 2017 Thunderbird Forum posts:
"Don't jump and spend money on something that may not be correct. I just checked on another owner that had the same problem [Tbird
A/C blowing hot air]:
He said, "The
coolant control valve is located on the passenger side of the
radiator shroud. You will find three hoses connected to it, two of those hoses running to the heater core, the other routes to the upper
radiator hose. This
coolant control valve has two electronic actuators that divert the coolant in the appropriate manner. When they malfunction you will get only HOT air blowing from your vents regardless of which temp you set, whether
A/C is on, or where you direct the air to come from. The
part can be ordered from Direct Ford
Parts for $102." -
Installed it himself. Not sure if this is your problem, sounds like it. But, always refer to the
search function.....There's a wealth of info there for you."
Retrieved 5 July 2017, from
http://forums.fordthunderbirdforum.com/threads/a-c-blowning-hot-air-help.3549/#post-30456
See also,
Doering, R., Horne, T., Horne, T., & Horne, T. (2017). 2005 T'Bird AC Only Blows Heat. Ford Thunderbird forum covering all models 1955-2005. Retrieved 5 July 2017, from http://forums.fordthunderbirdforum.com/threads/2005-tbird-ac-only-blows-heat.5280/#post-32648