Getting temperature estimates at finer resolution than 1 km is not likely to happen without you placing your own temperature loggers around your study site. You're going to have to look into using different explanatory variables. If you hope to be able to determine any drivers of distribution in an area that small, especially for wildlife (vs. plants because they don't move!), you will also need to look for higher resolution data. Even then, I'm skeptical you will find anything just using presence data from such a small area.
But to answer your questions, I would recommend checking out Planet Research and Education account where you can download some amount of high resolution (3 m) imagery for free. If you are affiliated with a university or other research institution I would start there. Next, Sentinel-2 can provide data at ranges from 10 m to 30 m. Finally, I would also recommend Landsat for 30m resolution.
Since temperature estimates at resolution finer than what you've already found are not likely to be available (without considerable uncertainty in those estimates), you will need to focus on other drivers. Using Landsat you can get elevation and some derivatives such as slope, aspect, and wetness indices. Using Sentinel-2 and Planet imagery I would recommend looking into vegetation indices such as NDVI, NDRE, and CLRE. If you have other habitat information, even in vector form, such as water and vegetation cover type you can include those in your model as well.