Plenty of guys run without fan shrouds, but I'm a firm believer in the benefits them.
You said your fan was turning, but was it actually engaged or just freewheeling? With the engine off, you should be able to turn it by hand, and you should feel some resistance, kinda like it's turning in gooey molasses. The clutch contains a temperature-sensitive silicon fluid, and some fans can be taken apart so you can replace the fluid. I don't have a part number, but you should be able to find it at any Toyota dealer.
