Bash - How to output two commands to file?

Something like this? (In a loop, cron, or whatever you're currently using.)

(date; my_sensor_command) >> log_file

Group all commands in parenthesis, because that will execute them in a sub-shell which you easily can redirect the output from:

 while sleep 5m
 do
         (date +%Y-%m-%d_%H:%M | tr -d '\012'; echo -n ' '; \
         /etc/rc.d/init.d/lm_sensors status | grep '^CPU Temp') >> /your/log/file

 done

If I understand your question right--you want to output two values to the same file--then this might be what you are looking for:

TIME="`date`"
SENSOR="56"

echo "$TIME $SENSOR" >> /path/to/a/file

Maybe I am misunderstanding the question, but it looks like all the answers are appending to one file. I read your question to be that you want the same output in 2 files. If that was what you are looking for, tee is a way to accomplish that:

echo "Stuff to output"|tee -a file1 file2