Please check the link on how to run a command on boot using cron. That should help you to start your binary on boot.
How to write a initial script and let it run a command automaticallyHow to write a initial script and let it run a command automatically
sudo crontab -e @reboot /home/pi/temp_logger/temp_logger This should be sufficient to run your cron job and I don't think you need that
"./temp_logger"
Also you don't need the "&". This is generally used to put a process in background. The only thing that you need to take care should be proper logging to debug in case of failures. I hope you have done that.