Yes, it's uncomfortable.
No, it's not a concern.
My personal experience (having traveled many thousands of km/miles in the summertime as a child) is that high temperatures while driving is not a serious concern. When you don't have A/C, then your best defense against heat is to be smart:
Passengers will be thirsty.
- Bring lots of drinking water, but avoid sweet drinks and soda.
Passengers will sweat.
- Place a fluffy towel on each seat, from the knees to the shoulders. It's not so much about absorbing the sweat but more about adding a thin ventilation layer between yourself and the seat.
- You'll need fresh air, and even if it's warm outside it will likely be warmer inside, so run the ventilation one or two notches higher than usual. Don't run it at full speed the whole time, that's very uncomfortable.
- Unless you're driving very slowly, avoid opening any windows. The drafts can be very uncomfortable and even painful to the ears. Besides, the car's ventilation is better suited to actually ventilate the cabin in terms of getting rid of the old air.
- Bring a spare t-shirt to change either along the way, or at the destination.
Keep the sun out.
- As much as you safely can, block the rear side windows with a cloth diaper or similar. Roll down the window a little, put the top edge of the diaper over the window's edge, and roll it up again; the diaper now hangs down on the inside, blocking the sun from the passengers.
- You can also buy suction-cupped window shades but IMHO these don't stick well (they suck because they don't, haha) and they don't cover enough of the window surface.
- Don't drive through Death Valley.
- Try to avoid driving during the noon hours (approx. 11:30-14:30) where the sun will hit you the hardest.
- Consider that on a road trip, one side of the car will usually get all the sun. Periodically swap places so that all passengers get a break from the sunny side.
Passengers will be tired, and stressed.
- When it's hot, taking rest stops frequently is even more important. You need to get out in the fresh air, chase each other around the car five times, hit the rest room, maybe buy an ice cream, and get back on the road again.
- Bring fruits and other snacks that handle heat well. Avoid M&M's...
Of course all of the above applies to the driver as well but I wanted to focus on the kids' well-being.
My national drivers' association has an interesting recommendation for those who have A/C:
Don't set the A/C more than a few degrees colder than the outside temp
because entering/leaving the car is more brutal to your health than
the actual temp in the car. [paraphrased]