First of all, having the display on and especially charging your device are the two biggest sources of heat. The Kurviger app itself runs with a rather low resource and battery consumption. When following a couple of best practices, it is easy to navigate without any overheating issues. There are reports on the internet were people report about overheating smartphones when using them as navigation device for their bikes.
First it is important to understand, that just because your smartphone feels hot, does not mean it's overheating. Smartphones are built to withstand heat. Usually they will start throttling the CPU/GPU at around 40°C (105°F). Which is still not an issue for your phone. Most phones have a safety switch and will switch off / restart if they get to hot. That is what most people refer to as overheating, as long as your phone does not start to behave unexpected or restarts itself, everything should be fine. When unsure, please turn off your phone and let it cool down in the shade. Please also refer your smartphone's manual or contact the manufacturer to make sure that your smartphone is able to withstand these conditions.
We recommend not to charge your phone while navigating. Charging creates a huge amount of heat. We recommend to charge your phone during breaks in the shade. Phones equipped with “Quick Charge (QC)” in combination with a QC charger or power bank should be fully charged within one hour. Furthermore, when buying a new mobile phone, you should pay attention to the protection class IP67/68.
Another reason for overheating phones are closed phone cases and closed phone mounts (often waterproof). These cases will similarly to a greenhouse heat up your phone but there is no way for the hot air to get out. Using an open phone mount will massively reduce the heat of your phone. Some waterproof cases have the option to keep them slightly open, without introducing the risk of you phone falling out, this can also help with cooling down your phone.
I personally navigated with the Kurviger App on my phone in Australia with air temperatures above 40°C (105°F). I had no overheating problems. I did not charge my phone while riding and I had an open phone mount.