This happened to me during my maiden voyage back home after getting my new engine/tranny/turbo installed. During the install, the fan shroud got broken in little places, but it still appeared to be intact. While driving though, the fan contacted the shroud and completely annhilated both the shroud and the fan. I had severe vibration at most speeds, and of course it was a mess in the engine bay (plastic EVERYWHERE!)
All I ended up doing is remove the remnants of the fan and the shroud, and instalied an electric fan from the parts store (2400 CFM flow), and shimmed the water pump pulley bolts about 4 shims each (the better way to do this is to buy smaller bolts, I think they are 10mm). Wire up the electric fan (I don't know the wire to connect to on an 87 like yours, just my 90), and you're good to go.
However, you have a much bigger problem. Buy a block tester at NAPA or somewhere, you likely have a BHG. There is no reason for the car to smoke and overheat (like a BHG does) when your car's fan is damaged. Although the reduced flow will make it run warm, a BHG is more likely to be your problem.
If indeed it is a BHG, you have several options (and of course, this is the most talked about problem of any Mk3 supra, EVER). You can purchase a ready to go motor from places like jarcoinc, maxx autoworks, and many, many others. The guy that did my car probably has a few engines left over, as all he does is install 1JZ engines for these cars. Which brings me to another option, install a 1JZ engine. This is much more complex, but the rewards CAN be great. Finally, you can attempt to repair your engine entirely, and reinstall either a factory improved HG or go with a metal head gasket and ARP bolts, and a whole mess of other things that go with installing a MHG. You have to machine and ap the head and possibly the block, test out a lot of measurements and make sure the engine is still stable. Lots of variables there, so it can get tricky.
Since this is one of your first posts, I need to direct you to read the sticky's about all this BHG stuff, and about MHG's too. In fact, read every sticky about this car if you can. This car will bite you in your ass (thats where your pocketbook is, right?) if you don't watch it.
Rundown of costs estimated:
New 7MGTE engine complete with MHG and ARP studs, ready to go - $2200 at
www.maxxautoworks.com Others here can probably do better for less money, but you must ask.
Rebuilding your motor with stock HG - between $500 and $2000, depending on what is damaged or worn in it.
Rebuilding your motor with a MHG - between $750 and $2500, again the same variances
Replacing your 7M motor with a 1JZ twin turbo engine - between $3000 and $5000, depending on your luck and your shopping prowess.
These estimates DO NOT include labor to install and remove parts, but do include the cost of machining and lapping.
Bottom line (if you've read this far you must still want to keep this car), you're gonna have to spend some money either way, so get ready and good luck, may your expenditures not exceed your expectations!