This is assuming no stirring, since that is a hassle.
There is a third possibility of pouring both in at the same time. That would ensure the fastest convection.
Cold then warm will be slowest since warm water rises.
Warm then cold will be slightly faster since it promotes convection.
This all depends on your personal preferences.
The fastest route to the correct temperature should be pouring both at the same time. You can guesstimate the end temperature by volumes. If they start at the same volume, then they will meet at the middle. The fast convection rate will ignore most of the effects of the room temperature at first.
Depending on which you hate more, I would stop at more favorable of colder or hotter than the goal. Test and add more water.
Edit: If this is for drinking and you don't mind a roundabout way and some effort.
- Refrigerate a pitcher of drinking water so you know its temperature.
- Find out the temperature of the hot water.
- Figure out the volumes necessary to reach your desired temperature.
- Etch/mark the level into a drinking cup for the waters. Remember the order.
- Pour separately and stir.