ireuel
Requirement of PWHT / PFHT for this case has nothing to do with temperature drop. I would suggest you go over the following article. You may clearly see that heat treatment for anhydrous ammonia service is only a measure of SCC control.
http://www.nationalboard.org/Index.aspx?pageID=182"Filling of empty tank" when tank is opened / not under pressure with any volatile (low boiling point) liquid leads to temperature drop towards liquid's saturation temp. whether it is "in sun" or not.
In that situation you shall follow code requirements and restrictions (UW-2 ; UCS-66 ; UCS-68 etc.)
SCC attack of Heat Affected Zone at a top of ammonia tanks caused due to air contamination, as ammonia tanks max. permitted filling is 54%-57% (DOT specifications).
There are some other situations that PWHT is recommended due to operating conditions of dynamic loads / temp. cycles, when residual stress is problematic even though it's not prohibited by a code requirement. For example:
http://www.nationalboard.org/Index.aspx?pageID=180