MC was sent back in time several thousand years. Ends up in the Mediterranean region that is mostly dry as an ice age has bound most water in huge icecaps. He befriends a large cougar type cat (horse size) that I believe he names "Pard". The two may have even be able to understand each other by a type of telepathy. I know this isn't the normal request on the site, but I'm going crazy trying to remember who wrote the book.
I made a huge mistake! I went to look up both suggestions made below and got the mixed up on my iPad. I thought I was reading the Turtledove book and was actually reading "The Steel of Raithskar"
(Gandalara Cycle #1) by Randall Garrett, Vicki Ann Heydron
Sorry for the confusion. I didn't know what tab I was on when I started actually reading.