Have a 2000 ford ranger 2.3L 4 cyl w/ A/C…
It is running rough and water temp stays well below normal operating temp all the time. It is worst when first started, if allowed to just idle it runs smooth but when given gas it runs as if not all cyl are firing. When coming to a stop it dies. As the motor warms it gets better but not good, at least it stays running and if I let it sit at the stop sign at idle, it smooths out. I have changed plugs and wires and timing belt recently. My thoughts are in order of best guess (1.) O2 sensor. (2.) Vacume Leak. (3.) bad fuel injector. (4.) Water pump.
What direction do you think I should look?
I would first replace the thermostat and check the operation of the coolant temp sensor. The lower than normal operating temp suggests a stuck open thermostat. That will cause it to constantly run too rich. (But you check the coolant temp sensor too b/c if it is bad the computer will think its cool and it will still run too rich). This obviously needs attention so I would do that first and then see where things stand.
How are the fuel and air filters?
Is the check engine light on?
Did it do this before you changed the timing belt?
No, It ran fine before and after changing the timing belt