That's a great question. I guess we'd have to figure out if they knew to even "offer up" thought sins for forgiveness.
Ah, good question. The Torah is somewhat ambiguous about making sacrifices for "thought" sins, since all of the examples given of reasons to make sacrifices are for sins carried out in action. On the other hand, we know that Job made sacrifices for his children just in case one committed a "thought sin," so the idea was certainly not foreign to the Judaism of the 1st Century.
I've not done an in-depth study of this subject in the Mishnah and Talmud, but my impression based on what I've read so far is that only sins of action made one "liable" to make a sacrifice in Jewish law, but that the more righteous man might make additional sacrifices even for his thoughts as he was convicted. The rabbis certainly emphasize training one's thoughts to center on the Torah rather than on what a Christian might term "the lusts of the flesh," so there was certainly a cognizance of the idea of "thought sin."
The daily burnt offerings were thought to cover "sins of omission," missed opportunities to actively do good. I'm going to hypothesize that that would include missed opportunities to dwell on Torah instead of "fleshly" matters. I'll keep an eye out in my studies and see if I can confirm that.
Shalom.
That sounds pretty reasonable to me. Thanks for your response.