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Build Guide

For those who do not know what the templar quest is, watch the youtube video linked to the build. Keep in mind though that because the build used in that video is slower it will not clear the map as fast which makes it obviously less efficient. A few other things to remember are that space bar skips talking and so spam space whenever you are near an NPC, you can do 2 runs before you need to salvage, and if you accidentally click on the leader of the templar order (NPC in last room of the map) he will attack you after he finishes talking (so town portal while he talks then leave the game). If you do kill the templar leader you will complete the quest and you will not be able to do it again unless you restart story mode from the beginning (means you lose access to the best reusable parts farming spot in the game until you restart the story). Without this builds optimizations I was able to get this done in 1 minute giving me 100+ parts per minute but with this build, it took less than half that time (giving me 200+ parts in less than a minute). You can then convert those reusable parts to veiled crystal and arcane dust in the cube (just buy the blue/yellow items from vendors). I suggest casting gargantuan 1st, then big bad voodoo 2nd, and spirit walk last.

A full stash of rares = 60 mats if they are all rings/belts that only take 1 slot but normally you get an assortment and few of those are 1 slot rares so it would prob average at 34. That would require about 3 full inventory stashes for all 1 slot rares to get what you get from a double templar run but with the average being non 1 slot items you are looting at around 5 full inventory loads.
5 seconds per portal at 3 portals for 1 slot rares that = 15 seconds but since the templar quest needs 2 portals the remaining time loss is 5 sec if you have all 1 slot rares. However, as mentioned that never really happens therefore the average would be more like 7-8 portals leaving you at a loss of 25-30 seconds.
Now factor in the time it takes to pick up the items which may not be much but let's say you spend 1-2 seconds picking up/looting items to get full inv each run. Keep in mind now that a templar run means you get much more per item so you spend less time looting items to get the mats. All total I would say if the rares were already in 1 small area on the ground you might come out about even time-wise vs templar runs but that is simply never the case unless someone looted them and dropped them there for you which can not be counted since they could do that in a templar run just as easily.

To sum it all up for you if you stop looting rare/magic items and just do templar runs for the mats you want/need you will end up saving yourself and the rest of your party a ton of time. The only time this is not the case is if you are being carried and can not clear/kill the mobs yourself.