June will be hot on I-10 and up on 395 until you get some elevation around Tahoe. Watch your tires, especially on anything you are towing. You do not say if you are in a Motorhome, TT, 5er, etc. but as mentioned, fuel can be expensive and miles between stations. Some towns are only gas stations (Kramer Junction at 395/58 crossroad) and charge accordingly.
When you get off of I-15 onto 395 the first bit of road is a raceway during rush hour so try to go through later in the day. Have fun and watch your fuel gauge.
BTW: I-40 will be cooler on your return trip. You gain elevation after Kingman and do not loose much of it until you are dropping back down into TX.