Find and harass Paul
Check out the Air Museum on the west side of the base at 215 and Van Buren. That will kill a few hours. A little further south is the Orange Empire Railway Museum in Perris. Mostly electrical railway stuff, trolley cars, electric motives, a few diesels and a few steam engines. Have no idea what they might be running.
About 2 hours south is San Diego, even if for no other reason than it will probably about 15 degrees cooler, it's worth a trip. Zoo and museums in Balboa Park, The Model RR museum is probably one of, if not the best, in the country. Down on the bay - The USS Midway, and the Maritime Museum. At the end of Point Loma is the Cabrillo National Monument overlooking the bay, NAS North Island and the Sub Base.. That might be another 5 degrees cooler up there.
The Palm Springs Aerial Tramway takes you almost to the top of Mt San Jacinto.
It's gonna be damn freaking hot. In the winter there are a lot of interesting places in the desert. Ain't nothing interesting enough to go out in the desert if you don't have to right now.