Bicycle Mechanics - Old bike/new wheels compatibility

I have an early 90's Schwinn Tempo I pulled out of a friend's garage and have been using/abusing as a poor weather commuter for a couple of seasons--she needs some love. I would like to replace the wheels with a pair of Fulcrum 7s I have sitting around. They are Shimano 8/9 speed compatible and the Tempo is a 6 speed setup. What compatibility issues should I expect?

Also, the crankset is one of those oval-shaped Biopace jobs I've been looking for an excuse to replace, and if I need a new cassette I might as well do it all at once...recommendations?

The first thing you gotta check is the hub spacing. Older frames were 120mm, newer frames are like 130 mm to accomodate the extra gears. So, your newer wheelset might not fit the older frame. Sometimes you can spread the rear triangle by force enough to cram the rear wheel in, but I wouldn't recommend it. Maybe 3 or 4 mm, but not 10.
Then, your 6 speed derailler won't shift an 8 or 9 speed chain with consistency - especially if you intend to do index shifting. Chain is much narrower, and the distance from top jockey pulley to cogs is closer. All this stuff is engineered by the manufacturer to interface just so in order for the index shifting to work right. You probably know you have to be careful when upgrading - even with the same manufacturer. 15 years, plus 6 to 9 speed, plus who knows mis-matched manufacturer. More trouble than it's worth.
I've seen it done. It ain't easy, but people with bikes that have deep sentimental value go to unbelievable ends to keep it going.
Why not go to 7 speed? You should be able to squeeze an extra gear in there. And, since you don't like Biopace, install a new triple crank - with carefully chosen rings! This will help minimize gearing overlap, and 21 speeds is plenty. My Schwinn Hybrid is 7 speed freewheel (13-21), Huret front and rear deraillers, and the crank has hand-picked rings 46(alloy), 36(steel). I've never needed more gears, and I've had it 5 years now.

If your bike came as a 6-speed, the dropout spacing is likely to be 126 mm so the stretch to 130 for current 8/9/10-speed isn't that much. Some riders just leave the spacing as-is and struggle slightly to fit/remove the wheel each time. Others have the frame "cold set" to make wheel installation easier. In fact, by the early 90's some frames were already 130 mm or 128 mm to allow 6/7 or 8/9-speed wheels to be used interchangably.

You will likely need a new bottom bracket along with the new crank but your bike is English threaded and has a 68 mm bb shell so finding suitable replacements will be easy.

Thanks for the replies so far. I messed around with the bike/wheels and found it fairly easy to pry the frame onto the wheel--I definately didn't flex it 10cm, but it wasn't a "natural" feel either, so I'm guessing the spacing is 126mm. It's not too much to do every time I pull the wheel off.

So, now I have to figure out the cassett and gearing. Is it possible to put the old 6 speed cassett on the new wheel and use the same chain? Would some type of spacer be necessary if I did this? I don't feel like I need more than 12 gears unless it makes the switch easier for some reason.

And as for the BB and cranks, would a modern Ultegra crank work? (I found one in good shape on CL for $30).