Right Gear for Shooting Interviews in Rural Asian Summer Heat?

Greetings! I am hoping that some of you might be able to advise me about the proper kit for my purposes.

I am an amateur photographer and videographer and professional academic who works in rural subtropical areas, often during the summer, when heat is typically well over 105 F/ 40 C, then when the heat breaks it rains for a month or two at a time.

I have won several amateur photography competitions with my travel photos shot on a Nikon D90, and want a new DSLR quality or equivalent camera to take into the field.

For work purposes, however, I also need to be able to record uninterrupted video interviews. The problem was that my Nikon D90 would overheat and I often couldn't record for more than a minute or 3 at a time. Very frustrating! I wish I knew about this overheating issue before I went to the field last time...

I am looking for a single relatively small, lightweight, combination DSL quality or equivalent camera and video camera that I can take on my travels.

Camera: I've identified the Panasonic DH4 as a possible choice for me, since it shoots continuous video and supposedly does not overheat. Will it work for my purposes? Would you recommend any other cameras to compare it to? I also haven't heard much about the GH4's photo quality though. I would have ideally loved to shoot with a full frame DSLR. Does this camera even come close in photo quality? Any choices for less than $3k that do?

And speaking of kit, if I did get the GH4 what would I need to kit it out with?

Lenses? Any recommendations? Something relatively compact and modest will do, no big zoom necessary, but something with a little range perhaps...

Mic? I think I may be able to do without an external microphone as audio quality is not a big issue, since if I ever show these videos they will be subtitled. Also, I do not want to make rural folks in central India uneasy by clipping mics to them. Thoughts? All I need to do is be able to hear all the audio myself in post-production on close listening, so that I can translate and subtitle it...

Bag? I've been thinking about this a lot. I'd like to be able to pack my camera in a day bag that does not attract much attention & doesn't announce itself as a camera bag. I'd also like there to be enough room to pack a lunch, water, bug spray, sun screen, a spare t-shirt, light raincoat, a notebook, and other odds and ends.

Protection against elements? I'll definitely be carry silicon packs to fight humidity. Maybe also ice packs to keep the camera cool in the bag? Or are ice packs a dumb idea?

Overall I'd like to spend spend not much more than $3k...