Thermostat should be in the housing under the distributor on A series engines - though I could be wrong - been a while working on the A series. On the newer Corollas - they are in the lower radiator tube.
Two things to check - fuel and fire. Make sure you are getting fuel to the injectors - could be anything from a weak to clogged injectors, too low of fuel pressure, clogged fuel filter, hole in fuel line, or bad gas.
Ignition (fire) - I\'d pull all the plugs and read them (check for plugs that show excessive wetting (no ignition), fouling, etc.) Could be anything from plugs, to plug wires, distributor (cap and rotor), coil, or grounding issue somewhere.
After these - it would be a sensor (O2 sensor, ECT sensor, etc.), emissions (clogged cat, clogged EGR, etc.) or vacuum related issue.