Even though my truck is not overheating, the temperature gauge will shoot up to hot and the oil light will come on. After a few minutes, the truck will not let me accelerate anymore. If I shut the truck off, it will reset the oil light and the temp gauge and run fine for a while. But eventually, it will do the same thing again. Is it a sensor or computer problem?

There could be a few different issues that could cause the temperature gauge on your 2008 Ford Focus to read hot when the engine is not actually overheating. Here are a few things to consider:

Failed thermostat: The thermostat is responsible for regulating the flow of coolant through the engine. If the thermostat is stuck in the closed position, it could cause the temperature gauge to read hot even though the engine is not overheating.

Failed temperature sensor: The temperature sensor sends a signal to the temperature gauge to indicate the engine's temperature. If the temperature sensor is faulty, it could cause the temperature gauge to read hot even though the engine is not overheating.

Wiring issue: If there is a problem with the wiring that connects the temperature sensor to the temperature gauge, it could cause the gauge to read hot even though the engine is not overheating.

To determine the cause of the issue, it may be necessary to perform some diagnostic tests and possibly replace some components. A mechanic or a professional auto repair shop will be able to diagnose the problem and recommend the appropriate repairs. It's also a good idea to keep an eye on the engine temperature and take note of any other symptoms or issues you may be experiencing. This information can help the mechanic diagnose the problem more accurately

Is coolant system full of liquid ? Have you replaced the thermostat yet ?

When you have a check engine light, there are codes stored. That's where you start--with the codes

you have overheated the engine maybe thermostat or water pump fault

have the cooling system checked for air lock
will be a gauge sender not a sensor

Have you checked the engine temperature when the gauge shows fully high if it is true message and not lying and the problem is the temperature gauge? Since this happened stop the car open the bonnet touch the radiator hoses and even with off running engine touch the vents of the radiator to all surface and see it the temperature is everywhere the same.

try taking the thermostat out, see if it still gets hot, if its a vg30 engine, there could be trapped air in the system, there is a bleeder valve on one of the heater hoses, passenger side, right at the firewall

Air pockets will make the guage do that, and also cause your heat to come and go. Also, a poor radiator, as in rotting, or plugged up, will cause high temperature issues.

You need to have it checked, because you will blow up your motor, if the exhaust is plugged.

As a safety measure, fit a new thermostat and senser. Then top up with antifreeze and water pertaining to where you are.