Satellite ocean near-surface air temperature data
This is not a definitive answer but a few points from someone who has spent some time with remotely sensed temperature data.

I guess your best bet to get high spatial and temporal resolution surface air temperature would be to get reanalysis data from weather models and augment it with weather data from ships.

Purely satellite retrievals of surface air temperature are not very reliable as this is a rather indirect measurement. Consider Level 2 AIRS 50 km (approx. 0.5 deg) Surface Air Temperature data layer (https://disc.gsfc.nasa.gov/datasets/AIRS2RET_V006/summary?keywords=airs%20version%206). The spatial resolution is much lower compared to surface radiative temperature products. This is in order to compensate for the uncertainty in the atmospheric state and for lower resolution of the sensor that needs to balance its very high spectral resolution with lower spatial resolution to achieve usable SNR levels in each spectral channel.

Speaking of the reanalysis data the NCEP Global Data Assimilation System has 1 deg (approx. 100 km) spatial resolution. However depending on the region of study you might get higher resolution from regional weather models provided by local meteorologists. So you could start with the NCEP data spatially interpolated from 1 deg to 0.01 deg as an initial approximation.