Left side panel has a red blinking box with an arrow showing down to the temperature Gage what is this

Two heavy gage red wires one from the battery the side goes to the starter . The other is red with a light blue stripe ( small gage wire) Goes to small terminal . Starter solenoid located on inner fender ,engine compartment , not on top of starter ?
You can go to www.bbbind.com/ for free wiring diagrams . On the home page click on technical information five box will come up . Click on tsb's an free wiring diagrams . On the next page go to bottom an click on I agree . Next page click wiring diagrams an then enter your vehicle make, model ,year , engine size. Then under system click on engine , then subsystem click on starting ,then click search . Then click on the blue links one at a time . Do you know how to read a wiring diagram ? At the top you can zoom in closer an on the sides click on the arrows to expand the diagram right an left . The first diagram if you look on the left side near the battery you will see the starter relay has three wires going to it. Good luck hope this helps >

Your temp.gauge is probably bad ! Check for voltage at the coolant temp. sender ! You have to check it with the engine running . The red with white stripe should have a voltage the other wire ,yellow with red stripe is ground side ! Instrument panel fuse box fuse # 15 a 10amp fuse powers the gauges ,if your gas gauge works it's not the fuse . The dome lights get there power from an other fuse an circuit ! Did you check the bulb ? Check fuse # 8 IP fuse box , also a 10amp . Check for voltage at the dome light ,switch on !

Its a system warning light for the following
engine coolant temperature is too high
engine oil pressure is too low
fuel tank nearly empty
check the dials to see which it is, it should go off when you start up unless any of the above are showing

Its the coolant level... you need to fill the coolant system...

:o( you're going to have to pull the radio out to see what they did. They probably added a wire to an inappropriate circuit to power the new radio or amp. I will paste your factory wiring colors below. If you now have an extra wire, that is the likely culprit. Trace it to see where they hooked it in. If it isn't going to the the fuse box and using an extra slot, make it so by connecting it to the cold side of the fuse and put an approprite size fuse in. To determine the fuse size to use, you can compare the wire gage to other cold side wires and use a fuse the same size as you see being used for similar gage wires. Let me know if you have more questions.

1996 BMW Z3 Car Stereo Installation Diagram
Car Radio Battery Constant 12v+ Wire: Red/White
Car Radio Accessory Switched 12v+ Wire: Violet/White
Car Radio Ground Wire: Brown
Car Radio Illumination Wire: Gray/Red
Car Stereo Dimmer Wire: N/A
Car Stereo Antenna Trigger Wire: White
Car Stereo Amp Trigger Wire: White
Car Stereo Amplifier Location: Passenger Kick Panel
Car Audio Front Speakers Size: N/A
Car Audio Front Speakers Location: N/A
Left Front Speaker Positive Wire (+): Yellow/Red
Left Front Speaker Negative Wire (-): Yellow/Brown
Right Front Speaker Positive Wire (+): Brown/Black
Right Front Speaker Negative Wire (-): Blue/Brown
Car Audio Rear Speakers Size: N/A
Car Audio Rear Speakers Location: N/A
Left Rear Speaker Positive Wire (+): Blue/Black
Left Rear Speaker Negative Wire (-): Yellow/Brown
Right Rear Speaker Positive Wire (+): Blue/Violet
Right Rear Speaker Negative Wire (-): Blue/Brown

scroll through the diagnostics using the up and down arrow in the right side of the radio till you reach the percentage of oil left then hold the CLR button which is the circle inbetween those arrows till it resets.

The red warning light is a box with two waves in it, an arrow pointing down and a T on the top indicates your Engine Coolant is low.

that is the low coolant warning, these sensors are noted for false readings, so if the coolant is ok then replace the low coolant sensor in the radiator side tank.