I just disconnected it for the time being, was my method OK (im totally new to wiring).

House wires (2 black and white)>Cheap plastic attic light>attic fan thermostat box.

The house wiring and the attic fan wiring was capped under the light and then piggybacked (stranded) to the light fixture. I removed the wire nuts and put the house wires (solid) directly onto the screws of the plastic light fixture. I put a yellow wirenut onto each of the attic fan wires and tossed the piggyback. Checked with voltage detector and no power to thermostat on fan and attic light works.

Is putting the solid wires directly onto the screws of the lamp OK or did it need stranded wires piggy backed again?

Also noticed the electrical box and everything was very warm.... surely because the attic is about 120 degrees.... is there anything I should do to assure protection from these elements?

I think you did the right thing. All the attic fans I've seen only have thermostats. In my old house, I put a single pole switch in line to give myself a "service shutoff" if I needed to oil the motor, check the blades, etc.

Not sure if your interested but you could install simple timer in place of thermostat and install receptacle at the fan. At Christmas time you can plug lights in along your roof. Also seen outside lights with a motion detector installed, obviously the height off the ground be a factor.

I would buy a new fan. I had the motor die on mine this summer. I didn't replace it right away and I noticed how hot the 2nd floor was w/o it. I went to local Grainger(supply house) bought a new one. Made all the difference. Wire a disconnect (switch) before the t-stat to shut down if needed. Simple,basic electrical 101.

Wire the t-stat like a single pole switch,that's all it does. Turns fan on and off.

Be sure the attic fan is equip with both a thermostat and a humidistat.

I'd remove it altogether. Attic fans, in many ways, cause more problems, or hide others.

Some real world scenarios I heard about from local remodeling contractor on his radio show include;
1) a gas water heater pilot keeps getting knocked out because the fan keeps pulling in air.
2) The house's cooled/heated air can gets pulled through the light fixtures to get the needed airflow demanded by the fan. Thus your energy money is being wasted.

Nothing is better than a properly vented (passively), and insulated attic.

Keep in mind the link applies to Arizona, so R38 won't help in high elevations, or freezing winter climates.

Here is a link that might be useful: Arizona roofing ventilation