Hello Juan Fernandez,
I recently bought a very lightly used KL7505 from a guy I met on the radio and found that it also had the same exact problem that you described.
I searched the Internet and was able to find a complete and accurate set of schematics for the KL7505. I found that the amp has two separate temperature sensors. One is a Si diode that is thermally tied to one of the RF Power transistors and the other is a very tiny, surface mounted Thermister R7 that's on the small PIC microcontroller PCB that's located behind the control panel. This is the sensor that is intended to monitor the ambient temperature of the amplifier's surrounding. The problem is that the designers located the sensor inside the fully enclosed interior of the box where it is not only unable to measure the temperature of the surrounding room but, it's (stupidly) measuring the much warmer interior of the box. What do you think is going to happen? That's right, the computer will think the ambient temperature in your radio room is very warm and place the amp into over-temp. shutdown mode.
The solution I arrived at was to temporarilly open the little control panel in order to expose the sensor to actual room temperature. This made the over-temp shutdowns disappear, thus proving my idea was correct.
The permanent solution was to drill a series of six small holes through the bottom metal cover plate positioned so the holes are below the small space in front of the CPU card. Then I cut a 30mm hole and mounting holes to mount a small computer 12V fan onto the bottom cover plate, located in a spot behind the CPU PCB. I tied the tine fan to a constant source of 12V inside the KL7505. This then forced exterior ambient air to flow over the small CPU PCB such that the surface mounted temperature sensor is now able to measure the actual room temperature. The shutdowns never happened again. I'm sure that if I ever tried to operate the KL7505 in a very warm room that the unit will go into shutdown because now, the surface mounted sensor is able to measure the temperature of the actual room temp. as it was intended to do by the designer. Now I use this amp all the time and I love it.
Good luck.