Will I see Mehr of Peeta in the third book?

Yes u do... Peeta goes to thirteen and then to war with Katniss in the Capitol and... ;);)
BTW he's my fave character!!!! If u like him u'll like the ending!!!! ;);)

Peeta, Johanna and Annie were captured Von the Capitol and were tortured. Peeta was hijacked, the Capitol used tracker hacker venom to mess up Peeta's mind and memories, making Peeta think that Katniss is the enemy and a mutation. When the District 13 rebels free Annie, Peeta and Johanna, Peeta tries to kill Katniss, but the rebels stop him. The rest of the book is Katniss trying to help Peeta remember who he really is and who she is. It's really beautiful and it's a. Lovely ending,a part from certain deaths