NiMH (which is what eneloop are, not NiCd) won't explode in heat you can survive in, but may suffer. The most likely effect is a significant reduction in capacity, most of which will recover on cooling and recharging. Reducing the drain on the flash batteries will help (e.g. by swapping between sets frequently, or only using the flash as much as strictly necessary.

The Li-ion camera batteries shouldn't get too hot and (unless they're very cheap no-brand replacements) will have a thermal cutout. They are much more dangerous if they do fail.

Keeping your spare batteries in an insulated container (or just wrapped in a fleece jacket) will limit their temperature rise before you use them. I wouldn't cool them below room temperature before doing this, but they could be wrapped in with something fridge cold. If you do this, be sure to wrap the batteries tightly in plastic (small resealable bags work well) to make sure that no condensation can reach the contacts.

Try to hold the camera and flash out of the sun as much as possible. If you're doing a walk-shoot-walk type of activity, I suggest taking the batteries out of the camera before packing it away and caring them separately. The padding of your bag is a decent insulator and will keep the heat in, allowing it to spread to the camera electronics.