git log remote without fetch everytime

I have clone git project once. I need to get all latest logs from remote server. I have updated .git/config as:

[remote "origin"]
        url = git://giturl.com/project.git
        fetch = +refs/heads/*:refs/remotes/origin/*

I am running git log master..origin/branch_name to get logs from remote server. But I am getting old logs from local server. Some posts suggested to fetch project first, then execute git log command. I just don't want to fetch every time on my local server. I need to get latest commits from remote server without fetching as fetch command is taking too much time.
Is there any possible way to get remote branch commits without fetching everytime, only just clone in beginning? Thanks.