I am not assuming anyone knows, but I thought this is a good question.

Will Temporary Companions supplement or overwrite current companions. I.E I already have a Humanoid companion when I get to Primm( heck maybe even a creature companion too), when I go into that one building to untie the deputy, will he override my humanoid companion?

erm.. maybe it just won't give you the option of recruiting him?

I'm sure mods will come out eventually that will let you recruit everyone, concurrently. (Like with Lucy, Syndey, Bittercup, Fawkes... )

He'll probably just be your companion untill you have cleared Primm and then stay in Primm. i doubt he will take your current companion away, and I don't think the companion wheel will work for him either tbh. Just my thoughts though...

It's confirmed the wheel will work for him, and yup he is just a temporary companion.

This is what I think will happen when gaining his help.He'll still help you but since he's not anyone majorly important to have,he'll leave after finishing the quest.That's I'm hoping will happen.

http://fallout.wikia.com/wiki/Deputy_Beagle I know he is a temp, but does he count towards max comanions?

I doubt he'll count towards your max companions, in Fallout 3 Paladin Hoss and Initiate Pek don't and will happily follow you around the Falls Church area even if you already have a human and non-human companion.

In FO3 (using the companion glitch) and leading around all temps

I had such a large faction that the game told me i had too many members and that i should kill someone lol.

people like the deputy aren't essential for completing the quest anyway (in the gameplay video, when he died, it simply said "find someone else to help you".) So even if they do count to total, and you can't recruit them, you can still finish the quest/game.

Yup, I understand that, I was just wondering how the mechanics of companions work, as I never used them in FO3, becuase they were more harmful than good...