I missed the wrench and have exited out of the furnace. Do I need the wrench or do I get an opportunity to go back later and grab it?

You'll get the wrench later, probably right after you visit the pipe factory. The sandwich won't be there, though... gross.

I gave my sandwich to Lamb. :-)

I missed it, too and I can't find it later. Do I have to restart the whole game? :/

It should still be there. It's in the workshop where you met Hobbins. You can't continue in the pipe factory without it, so you can't have missed it.

I did miss it and I left the factory. I couldn't get back afterwards so I restarted the game, after all...

I've played this a while ago, but if memory serves right - you ASK him for it.

Which is hilarious, since for lots of people it probably goes like this:

*tries to take wrench*
H: Leave it, it's mine !
*tries again*
H: Don't touch that !
(...)
F: Can I borrow this wrench ?
H: OK :3.

I do miss it too.

I stole it while he was busy turning off the alarm you set off for stepping on the elevator...
Good ol' point n' click, resorting to manic kleptomania rather than simply asking to borrow something >.<

If you miss the wrench the first time you're in that area then you can actually go back to that area later. After exiting the furnace room and going up the stairs. Go left a screen along the walkway. Then enter the door on the right. This puts you back to where you were at the start of the game and you can walk to the room with the wrench. Hobbins is no longer in the room too at this point and there's no Reich patrolling the area so there's nothing stopping you. Easy-peasy! You can return here even after leaving the factory floor (assuming you can do that without the wrench). Just use your card to get back up via the elevators (just tested this as I had a save at Doctor Burke's).