You can get the FSM from here:
http://foxed.ca/foxed/index.php?page=rx7manual#secondgen
Haynes also has a surprisingly decent manual for the FC.
First, use ONLY an OEM T-stat on 86-88 RX-7s.
A stock '88 radiator will have an air bleed screw on the upper radiator hose neck. You'll want to loosen it but not remove it. The air bleed screw and radiator drain screw are plastic, so be careful or they will strip.
The engine block drain plug is on the driver side of the engine just above the engine mount. Use a 14mm (IIRC) wrench to remove it. I start it with a combo wrench then finish it off with a 14mm socket and a skinny ratchet. Keep some newspaper/rags/what have you handy since the coolant will splash off of the engine mount and make a mess. You may need to unplug the spark plug wires to get to it; make note of how they were plugged in. Mixing up the spark plug wires is bad juju on rotaries.
Keep the radiator pressure cap on and fill the coolant from the thermostat housing. Crank the heater all the way up, start the engine, and let the coolant circulate. Keep adding coolant until it starts to seep from the bleed screw, then close the screw. If the coolant alarm buzzer keeps sounding, keep filling the radiator slowly from the thermostat neck until it shuts off, then add a little more.
Don't call it a rex. Subarus and Mazdas both will get angry at you. This may be your whole problem.
You are using coolant mix, right? Not straight water? The rotor housing temps reach 400 degrees near the spark plugs. This will boil pretty much anything you can throw at it, but a proper coolant mix will fare better. Water transfers heat better, but it can't transfer heat if there's an insulating layer of steam preventing it from contacting the metal, so you need at least 50/50 in there. And a decent water pump.
If your thermostat doesn't have a bleed hole, put one in there, and make sure it's clocked at the highest point (towards left side of engine).
I have never had a Mazda rotary with air bleed-out problems. (I have also never had an FD) The water pump housing is actually a very good design, and they were kind enough to put a bleed hole between the pressure and return sides. You have an FC, so it is possible that aluminum corrosion has gunked this bleed hole, though I've never encountered problems other than DSM-like pitting at the lower hose connection.
Is the gurgling from sucking in coolant from the overflow tank while the car cools down?
If so, then that is OK.
If you have a plastic filler neck near where the radiator cap screws on, check it for cracks.
In reply to amg_rx7:
Oh, that reminds me! My series 1 RX-7 had a swollen hose inside the overflow. It expanded enough to seal itself to the bottom of the tank, acting as a perfect check valve. Later, it lost its seal against the cap, so it would noisily slurp air in as the engine cooled down.
Granted, that's a car that was eight years older, but this was eleven years ago.
