What P0113 means
Your car has a sensor that measures the temperature of the air coming into the engine, usually called the IAT sensor. It's often built into the mass airflow sensor, sometimes it's a separate part in the intake tube. The computer uses this reading, along with a few others, to figure out how much fuel to add and how to adjust timing. P0113 means the computer is seeing a voltage from that sensor that reads as "too high," which usually translates to an air temperature that's impossibly cold, like the intake air is colder than it could realistically be. That's a signal the circuit isn't behaving, not necessarily that the sensor itself is bad.
Is it safe to drive
Yes, generally. This isn't a code that causes stalling or sudden loss of power. The computer usually falls back to an assumed default temperature value and keeps running the engine reasonably well. You might notice slightly rougher cold starts, a little more hesitation on a cold morning, or a small drop in fuel economy. Keep an eye out for the check engine light changing to flashing, or any new symptoms like stalling or misfiring, which would mean something else is going on and it's worth getting looked at sooner. Otherwise this is a fine one to schedule normally.
Common causes, most likely first
A wiring problem is the most common cause: a loose connector at the sensor, a corroded pin, or a wire rubbed through somewhere in the harness, especially if there's been recent work near the intake. After that, the sensor itself can fail internally and read wrong. Less commonly, it's an open circuit or a poor ground connection back at the computer. On some vehicles, an aftermarket cold air intake or a MAF sensor that wasn't seated back correctly after cleaning can trigger this too. Which of these is likeliest depends on the engine and how the IAT sensor is wired into it, so we wouldn't guess without looking.
What diagnosis involves and rough cost
Diagnosis starts with pulling the live sensor data on a scan tool and comparing it to actual conditions, then checking the wiring and connector at the sensor with a multimeter, looking for voltage that doesn't match what a good sensor should show. That usually takes under an hour if the wiring is accessible. If it turns out to be a connector or wiring fix, that's a relatively inexpensive repair. If the sensor or the MAF unit needs replacing, cost depends on the part, since MAF/IAT combo units vary a fair amount in price by make and model. We can give you an actual number once we know which it is. This isn't something we'd recommend just throwing a new sensor at without checking the wiring first, since a bad connector will make a new sensor throw the same code.