Hi Justin,
Outside of the absolute maximum ratings, the part may malfunction, whereas outside of specified range the part may not meet the specs defined in the electrical characteristics.
Take a look at the OPA827 (http://www.ti.com/product/opa827), which has a specified range over -40 to +125C. The output can drive up to 10.6Vrms. This is because the output can swing from (V-) + 3 to (V+) -3, which is -15V to +15V max, which is Vpp/2/sqrt(2) = Vrms = 10.6V.
Please let me know if you have further questions. Thanks!
Regards,
Brian Wang
