Tough one to answer. For header pins, a 40 watt iron is probably fine. If you were trying to do something smaller, I'd say no. The problem you'll run into is you have no temperature control and some pins need more heat than others. For most of the pins, the iron will be plenty hot and you'll need to limit the amount of time you heat the connection. Some of the ground pins have large contact to the ground traces and soak up the heat and you'll need to heat longer to get the solder to flow.

As for reflowing, it may do the trick since most of the traces are on the back of the board. That being said, it is best to remove the solder entirely, clean, and replace it with new solder. The new solder and flux wet much better and flow into the joint better than just heating up what is there. The problem you will run into is System 3-7 pins are tough to remove without a good desoldering tool. A solder sucker doesn't pull out the solder very good and if you have to heat and suck several times, you can lift a trace.

Maybe Hans will chime in. He's the System 3-7 expert.

After all that, I'd say give it a shot. The header pins are more forgiving than a lot of stuff.

Give it a shot. You probably won't hurt anything and you'll probably fix it. The CPU display pins don't have any large ground connections so my talk about them sucking up heat is not really applicable in this situation. Good luck.

Give it a close up visual check. Most of the time you'll see a crack when solder is the issue.

I've had situations where there was nothing visible but reflowing the solder fixed the problem as well. I would recommend getting a temp controlled solder station. They are not real expensive and will be easier in the long run. If you are going to replace say a resistor or transistor that went bad the soldering station is an excellent thing to have.

On this era of machines, I desolder the connectors completely and resolder with fresh solder. But, that is best done with a vacuum desoldering station. I use a Hakko 470w on my bench, a Hakko 808 on the road.

Take the board off and look real close at the back of the pins. If you see what looks like a fine circle around the pin, that is a cracked solder joint. If you can't suck out the old solder, at least add a bit of new solder when you reflow the old.

Radioshack sells a desoldering iron with a built in sucker on it for about $15. It has worked fine for me for over a year now.

Either way, it is easy to do. Just don't let the iron sit on the trace any longer than it needs to.

While you have the board off, you might as well reflow the solder to all the pins. If one is cracked, some of the others may be too.