Just say, “my days of not taking you seriously are certainly coming to a middle.”
WHAP
“Just being fisty, what were you looking for?”
Excuse the hijack, but I did this just the other day to someone that was annoying me. I giggled when I saw it mentioned here.
It had the desired effect.
I think my only major caveat would be, “Do you need this temp service?” Temp services are notorious for their blacklists. If you do tell off this obnoxious worker, is there any way that can get back to the agency? I have worked temp jobs, hated them, and yet now that I’m older I just think…“don’t cut off your nose to spite your face…this asswipe will still be employed next week…you won’t…” The only rule about working temp, if they ask you to smuggle drugs, just say, “Heroin is my speciality…however, I can also smuggle cocaine for you…”
Here’s how I think the conversation should go.
Co-worker: So, what’s this about your dog?
jarbaby: What?
Co-worker: I overheard you on the phone.
jarbaby: Why do you want to know?
Co-worker: Just being nosy.
jarbaby: Oh. Okay.
—pause, while jarbaby looks at co-worker; when no further conversation occurs, jarbaby returns to what she was doing—
Co-worker: So, what about your dog?
jarbaby: Hmm?
Co-worker: I was asking about your dog.
jarbaby: I know. Do you have a better reason than “I’m nosy”?
Co-worker: Uh, no.
jarbaby: Right.
—back to what she was doing—
I guess that tack would work… if I were dealing with someone who had normal social skills. 
Actually, he’s the tech support guy in this office, so I’m sure if he realllllly wanted to know what was on my screen/hard drive, he’d have no problem getting around a screensaver password. (I’m also not in this office more than 2-3 days a week, so he’d have plenty of opportunity to snoop, too.) It’s also usually not worse than his staring intently at my screen for a few seconds. I don’t have anything incriminating on this particular comp, so I’m willing to put up with his occasional over-the-top nosiness in exchange for frequently picking his brains on technical matters.
On the other hand, if I EVER caught him poking about my laptop… he’d be learning how to type with hooks. 
Well…then maybe he’s not looking at WHAT you are doing, but just taking a quick peek to make sure everything is as it should be.
None of my coworkers know anything about their computers, and I get called over to help them do everything from sending and recieving email, to navigating on the Intraweb thingy, and all sorts of things in between. I have gotten into the habit of just kinda taking a peek around their desktop and taskbar whenever I go over, just to make sure there’s not something weird going on. (Like the guy who usually opens his email box 5-6 times)
But…he could be nosy too 
Hitting a man with a banjo is dirty fighting. You want to knee him in the groin.
I have two words for you…
Stun Gun.
Usually, just the crack-crack-crack sound and the mini-lightning storm is enough to send even the nosiest snoop runnin for the hills, you don’t even have to shock 'em, though I would, just for general principles.
“oops, just being violent”
Well, the other reason I don’t go postal on this office is because of a long story where I’m trying to get a permanent position in another department of the hospital,through this temp agency. So I’ve got to be on my most professional behavior while they bounce me around to different departments for a while. THEY OWN MY ASS.
Clearly the guy’s testicles just dropped and this is the source of your problem. Remove them and my guess is he’ll stop hanging around. Right now, he’s just nuts about you.
I’m sorry, I didn’t know your job was through a temp agency. In that case, ditto Cervaise. Let us know if he doesn’t get the hint, and we’ll try something stronger.
Look at person with raised eyebrows and eyes opened wide.
Shake head slowly from side to side and bite lower lip while turning away.
Go back to work. If cow-orker persists, start shaking as if you are surpressing a laugh.
That’d get rid of him! 
Even more effective (at least from what I’ve read) would be spraying him with the asses of lieu’s coworkers…