Your engine is taking too long to warm up — the computer expected the coolant to reach operating temperature within a certain window, and it never got there.
That's it. The engine is not overheating. It's the opposite problem: it's running too cold, and the computer noticed.
Plenty of P0128s roll into my shop with zero symptoms besides the light. Don't let that fool you into thinking nothing's wrong.
Notice what's not high on that list: the computer. The PCM is almost never the problem, no matter what the forums tell you.
I hook up a scanner, pull the freeze frame so I can see what the coolant temp actually was when the code set, then watch live coolant temperature from a cold start. Coolant level gets a look first because it's free. If the temp crawls up slowly and flat-lines around 160–170°F instead of climbing into the 190s, that's a stuck-open thermostat and the diagnosis is done. I'm in Florida — if an engine can't reach operating temperature in our heat, that thermostat is wide open. If the live reading doesn't match reality — engine's clearly warm but the data says cold — then I go after the sensor and its wiring instead.
Honestly? Yes, for a while. This is not a tow-it-now code and it won't leave you stranded. But "safe to drive" isn't the same as "fine to ignore." An engine running cold burns more fuel, wears faster, doesn't cook the moisture out of the oil, gives you lousy heat, and can fail an emissions inspection in states that have one. Fix it in a few weeks, not a few years.
Broad ballparks — your exact vehicle changes everything:
Before you pay anybody a diagnostic fee, pull the code yourself. My app, Auto AI Diagnostics, reads codes for free with any cheap Bluetooth OBD2 adapter — the $30 ELM327 or vLinker type works fine. AXEL, the AI in the app, doesn't just spit out a definition of P0128. It looks at your car's freeze-frame data — the actual conditions when the code set — and explains what's most likely going on with your vehicle, in plain English or Spanish. Walk into the shop already knowing whether you're probably looking at a $30 thermostat or something else. That alone can pay for the adapter.