It can be screaming hot in June or absolutely perfect...it simply depends on various factors. As wrdjoh4 said, there is no shade and unless you have and run air conditioning with a generator which will likely upset those who are out there for peace and quiet you could be sweltering. More importantly, and in support of Bedoin’s insight the Covid19 thing is a far larger concern. The last I checked the Alabama Hills, despite being BLM, was locked down and closed due to the impact an onslaught of tourists might have on Lone Pine. (Not sure how they closed Movie Road, but that is what the BLM website said) Mind you I last checked in early May hoping to escape out there but things may have changed by now. Before heading out there check the BLM website.