The factory installed water pump on the Z3 has a plastic impeller which breaks causing catastrophic engine failures. So I decided to replace mine. While I was in there I also replaced the thermostat, belts, and hoses.
I found this write up to be very helpful:
1. The first hurdle is getting the fan off. Use a 32mm wrench and something to hold the pulley while unscrewing it. BavAuto and Pelican Parts were both out of the pulley holding tool (back ordered for a month) so I made one using a drillpress and a piece of metal that was laying around in my garage.
It's hard to see but the hole in the pulley holding tool is around one of the bolts on the pulley.
The wrench is on the fan nut and the pulley holding tool is holding the pulley in place. A bit of a tight squeeze.
Using these tools, the fan was relatively easy to remove. (Finding a good price for the wrench (amazon.com) and making the pulley holder was the hard part).
2. Remove the plastic shield from under the engine (4 screws).
3. The fan and the fan shroud need to come out of the engine compartment. The fan shroud is held in place with plastic fasteners (similar to a molly bolt) located at the top right and top left of the shroud. The inside (bolt like) piece must be removed (pried out (a small screw driver will work)), then the outer piece can be removed (pried out). In the picture below, my middle finger is on the hole for one of the fasteners (top left). The other one is located on the other side of the radiator (top right).
4. There are a couple of hoses that are attached to the fan shroud/expansion tank that must be removed. One of the hose clamps is near the top right of the radiator (see picture below) and is easily removed.
The other hose goes into the bottom of the expantion tank (see picture below) and is probably best removed by loosening the end of the hose that attaches to the engine.
Once you get the fan and the fan shroud out, you can access the thermostat and/or waterpump. If you haven't already removed the radiator hoses, now would be a good time.
5. To get to the thermostat, you'll need to remove the bracket that is used to lift the engine (see below). I've seen some threads where people have stripped the bolt the socket wrench is on in the picture below. Recommend marking that bolt with some paint, and checking to see what it is currently torqued to.
There is a bolt at the top of the bracket (shown above) and one at the bottom that is also attached to the thermostat housing (brown plastic piece connecting to the radiator hose shown above). There are 3 other bolts that hold the thermostat housing in place. Remove the bolts and the housing to reveal the thermostat (below).
At this point there's nothing holding the thermostat in except old age. I ran a coat hanger thru the thermostat (close to the spring), pulled hard with both hands, and it popped out. Be careful not to scar the engine where the new thermostat will need to seal.
You'll need to get the belts off. There are caps covering the allen wrench openings in the tensioners. It's hard to see, but there is an allen wrench sticking out of the accessory belt tensioner in the picture above. Turn allen wrench clockwise to release tension. A/C tensioner shown below (Also clockwise to release tension). The A/C belt must be removed in order to remove the accessory belt.
You'll notice there's a pipe on my allen wrench. It's unbelievable how much force is required to move the tensioners on my car.
Once you get the belts off, remove the 4 bolts from the pulley that sits behind the fan to reveal the water pump. Behind the pulley you will see the 4 bolts that secure the water pump to the engine block. Remove and replace the waterpump. Picture of old and new waterpumps shown below. (Be ready for some more water when you remove the water pump.)
Assembly is the reverse of dis-assembly.
There are a number of pages on refilling the coolant and bleeding the radiator. I refer you to those (including the link at the top of this page). I should probably mention that animals think coolant tastes sweet, if left in puddles on the ground, they will lick it up and die.