Brymen BM525 can log up to 87000 single values and 43000 dual values (it has dual display)..
It is 6000 count, dual temperature thermocouple measurements, AC+DC True RMS...
I bought it exactly for standalone logging .... it is something about 150€, there is a BM521 that has only one temp channel, and less data points...
Also, it is excellent quality, and has good overvoltage protection, so you can actually connect it mains power and leave it there logging without worrying it might explode if transient comes along.. Also with high speed min/max recording, you might use it to catch transients...
No Bluetooth though, you take to the PC after you're done and download data via cable..
But it seems to me you actually need logging thermometer..
As for temperature range, not many multimeters will go over 400C.. Not even all thermometers will... And not many K-type sensors will go that high, you'll have to buy one specified for such temperatures.