One problem related to radiator has been reported for the 2013 Honda CR-V. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2013 Honda CR-V based on all problems reported for the 2013 CR-V.
I had left my office about 10 minutes prior to pulling into a shopping center and was driving about 5 mph in the parking lot, looking for a parking space. I saw one and slowed down even more to barely moving, and was easing into the parking space with my right foot on the brake. Just as the car stopped and I was getting ready to put it into park, the engine suddenly revved up and the car jumped the curb and hit a tree about 5 feet in front of the parking space at full force. It was like the accelerator had been pressed all the way to the floor. I was totally stunned. The entire front of the car was smashed in and radiator fluid was coming out of the bottom of the car. When this incident occurred, I was not talking on the phone; I was not drinking or eating anything in the car; I did not even have the radio turned on. I was not in an emotional state; I am not psychotic, homicidal ,or suicidal. I had both hands on the steering wheel as I had just made a slow left turn into the parking space and was barely moving, with my foot on the brake. I have gone on the internet to research anything like this occurring with other Honda crv's, and there are numerous incidences cited involving the 2011 and 2013 models. It happens in very cold weather (freezing or below) , while the brake is engaged. It was in the low 30's at the time and my foot was on the brake. Luckily, the tree stopped my forward motion, or I would have ended up driving thru the plate glass window of the ups store. Other drivers have not been so lucky - some have been taken to the hospital, other cars involved, other people injured. I am absolutely terrified of driving this vehicle again.