It's entirely possible that your MAF is getting lazy when hot, but it's pretty easy to check. If you check your MAF g/s reading, it should be 1 g/s, per 1k RPM, per cylinder. So a 4 cylinder engine at 1k RPM should report AROUND 4 g/s unloaded. 8 g/s at 2k, 12 g/s at 3k, etc. The fact that your trims get higher at the engine warms is a bit strange, usually a warm engine is more efficient and therefore should mask most issues that cause high fuel trims.
High fuel trims indicate that the PCM is having to add fuel from it's base table to maintain a stochiometric air/fuel ratio as measured by the primary oxygen sensor. This is usually caused by a vacuum leak, however it can also be caused by a sticking EGR valve or improper valve timing.
I see P0172 (Bank 1 rich) codes all the time on the Toyota 1ZZ engines. It's almost impossible to catch them in the act, the root cause is shrunken intake gaskets that only leak when bone cold. After 2-3 minutes of running, the cylinder head warms enough to seal against the intake manifold and the fuel trims look perfectly normal.
End of the day, if you aren't throwing a P0172 code, my first stop would be replacing the B1S1 air fuel ratio (oxygen) sensor. This is the most likely spot for a "lazy" sensor to give erroneous readings and therefore skew trims and effect driveability.