over current in 26 AWG (pulsed)
It is nice to see all theoretical considerations and suggestions for experiments to determine thermal constant of insulated 26 gauge wire. Of course the precise result will depend on ambient condition, whether it is in still air or under some airflow, etc. However, all this work already has been done in Electrical Engineering, and results are well documented. For practical considerations I would suggest the following Wikipedia page. 

From this page, the 26 AWG wire will burn up at about 20 A in 10 seconds, and hold up to 218 A for 32 ms.

So, to answer the direct OP questions, there is nothing to worry about 3 A for a surge of 25 ms long.