Rim brakes also heat the rim because the brake functions by converting kinetic energy into thermal energy. In normal use and with lightweight bicycles this is not a problem, as the brakes are only applied with a limited force and for a short time, so the heat quickly dissipates to the surrounding air. However, on heavily-laden touring bikes and tandems in mountainous regions, the heat build-up can increase tyre pressure so much that the tyre blows off the rim. If this happens on the front wheel, a serious accident is almost inevitable. The problem is worse when descending cautiously at slow speeds because the brakes are "always on" and the cooling airflow over the rim is insufficient. The risk can be reduced by not over-inflating tyres and adopting an aggressive riding style, only braking for the corners, but the real solution is a drum brake or a disc brake which avoids rim heating.
wikipedia. how hot is hot though. need a new bike.