Thermostat is on the back passenger side of the engine. You will have to remove the right engine mount, accessory belt, and alternator in order to access the water neck that houses the thermostat. Get a mirror so that you can see where the water neck is located.
Should be located in the removable housing at the engine end of the upper radiator hose
Up next to the firewall on the bottom radiator hose, on the right side near the intercooler, on the MKII
Pictures and instructions are found here: http://www.padandwheels.com/mr2/thermostat/thermostat.html
in the tank
The Toyota mr2
by the oil dip stick
that is the oxygen sensor on the exhause manifold.
thermostat is by the engine. open up the engine hood. standing from the back of the car looking towards the front of the car. the thermostat is on the right hand side (passanger side) and runs from from a hose to the mount on the engine. It's under the water pump.
under the hood behind the spare tire.
behind the dashboard on the passengers side
The O2 sensor is located on the downpipe of the MR2, although you were not specific to which MR2 generation/model you are referring to. Most are located there. The downpipe will be bolted to the exhaust manifold, which is bolted to the side of the motor closest to the firewall.
The battery is behind the spare tire, under the bonnet.