Extending your BMW life and improving its performance

Inspect Clutch and Belt: Check the clutch assembly and the belt that drives the compactor. Look for signs of wear, damage, or misalignment. A worn-out clutch or a loose belt can cause the clutch to overheat and the engine not to rev up properly. If you find any issues, consider replacing the clutch or realigning the belt. Check Engine RPM Sensor: The engine's RPM sensor is crucial for the proper operation of the compactor. If the sensor is faulty or misaligned, it may not provide accurate RPM readings to the engine control system. This can lead to performance issues. Inspect the RPM sensor and its connections to ensure they are clean and secure. Inspect Air Filter and Fuel Filter: A clogged or dirty air filter can restrict airflow to the engine, affecting RPM and overall performance. Similarly, a clogged fuel filter can lead to fuel delivery problems, resulting in poor engine performance. Check both filters and replace them if necessary. Fuel System Inspection: Examine the fuel system, including the fuel pump and fuel lines, for any blockages, leaks, or malfunctions. Insufficient fuel supply can cause the engine to struggle with RPM. Throttle Cable and Linkage: Check the throttle cable and linkage to ensure they are not sticking or binding. A faulty throttle mechanism can prevent the engine from reaching the correct RPM levels. Engine Timing and Compression: If the engine timing is off or if there are compression issues, it can lead to poor performance and overheating of the clutch. Perform a compression test and check the engine's timing to ensure they are within the manufacturer's specifications. Inspect Vibration Isolators: The BPU 4045 compactor operates under heavy vibrations, and these vibrations can affect various components' alignment. Check the vibr
Check clutches and belts: Check clutch assembly and belt connecting compactor. Look for signs of wear, damage, or misalignment. A worn clutch or loose belt can cause the clutch to overheat and result in poor engine performance. If you experience any problems, consider replacing the clutch or resetting the belt. Check engine rpm sensor: The engine rpm sensor is required for proper compressor operation. If the sensor is faulty or incorrect, the engine control system may not be able to give an accurate RPM reading. This can cause performance issues. Check the RPM sensor and its connectors for cleanliness and tightness. Check air filters and fuel filters: Clogged or dirty air filters can restrict airflow to the engine, affecting overall rpm and performance. Similarly, clogged fuel filters can cause fuel supply problems, resulting in poor engine performance. Check both filters and replace if necessary. Fuel System Inspection: Inspect the fuel system, including the fuel pump and fuel lines, for blockages, leaks, or malfunctions. Insufficient fuel can cause engine rpm to drop. Throttle Cable and Linkage: Inspect the throttle cable and linkage for sticking or binding. A damaged throttle mechanism can prevent the engine from reaching the correct RPM range. Engine timing and pressure: If the engine timing is off or there are pressure problems, it can cause poor performance and overheating of the clutch Perform a pressure test and check the engine timing to ensure it is within the manufacturer's specification. Monitor vibration isolators: The BPU 4045 compressor operates under heavy vibration, and this vibration can affect the compatibility of components. Look at how it shakes

It is generally not recommended to bypass the oil cooler on a vehicle, as the oil cooler serves an important function in the operation of the engine. The oil cooler helps to regulate the temperature of the oil, which can have a significant impact on the overall performance and longevity of the engine. If the oil becomes too hot, it can break down and cause engine damage.

If you are experiencing problems with the oil cooler on your 1996 Ford F250, it may be best to have it repaired or replaced rather than attempting to bypass it. If you are having difficulty with the oil cooler, it is important to diagnose the issue and address it as soon as possible to avoid potentially costly damage to your engine

This says yes.

Oil Cooler for BMW 3 Series E46 (1999-2005) - Turner ...

https://www.turnermotorsport.com > BMW-E46-Parts > c-...
BMWs use an external oil cooler to regulate the temperature of engine oil and prevent a breakdown in viscosity and lubrication characteristics.

Assuming the fuel tank is breathing ok and there isn't a suction preventing the full flow of fuel, the tank is clean inside without water or sediment and the filters are clean, I only have one thought about your problem.

The fuel tank and the fuel in it is an essential part of the cooling system - the fuel return line carries excess heat from the fuel system back to the tank to be dispersed. A general rule is don't run less than a quarter full except on very short journeys or excessive wear will take place on highly stressed fuel system components.
This is more important with some designs than others and as many manufacturers utilising common rail diesel systems now fit fuel coolers it obvious they believe cool fuel is important.

This becomes more important when the fuel is a blend of diesel and bio-diesel, known to be a source of problems with the tight tolerances used in electric diesel injectors.

If your truck doesn't already have a fuel cooler I suggest you fit one.

60 k should include oil change, rotate tires, some filters (air, cabin air..etc), brake inspection, as well as a overall general check. Your next major maintenance will be at 100 k. Just keep up your reg. maintenance. You'll find the Toyota Matrix is a very dependable vehicle.