I decided to publish all this project under Creative Commons license (Attribution, Derivatives, Non commercial, ShareAlike). The source code contains a FAT12 filesystem that can be reused to make custom flash drives for other projects.
(PCB version 1.2, hence the misaligned 3.3V regulator to include a diode. Corrected in the V2.0)
You’ll find the schematics here: Simple USB temperature logger schematics
The Altium files (including a routed PCB) there: Simple USB temperature logger Altium files
The source code (based on Microchip Applications libraries -Device – Mass Storage – SD Card data logger- MPLABX): Simple USB temperature logger source code
The source code could be improved to increase the robustness of the logger (especially in the case of battery power failure while on logging mode). The PCB allows the monitoring of the battery voltage, it just needs to be implemented in the firmware.
I hope my work will be useful to someone!