KAPILLAI,

You Case 1 is appropriate. You should apply the operating temperature upto the shutoff valve of pump 3 shown in your sketch (apply the operating temperature to the valve also).

Case 2 is incorrect. You cannot apply ambient temperature to the complete standby line.

Also, as the stagnant fluid in the standby line will be in direct contact with the flowing fluid at the branch connection, it may slowly gain temperature through convective heat transfer. So, it would be inappropriate to consider an average of operating & ambient temperature unless you are completely sure of the thermal profile of the stand by line.

Regards,
ASA