According to the Motorola 68060 datasheet, there's nothing to indicate it does anything different when the temperature gets high. It does have a built in thermistor which you can use with external circuitry to sense the junction (die) temperature. If you got a bit clever with an op-amp, you could connect it to the analogue to digital converter in the joystick port, and write a program to display the junction temperature on workbench.
Don't forget you can disable parts of the CPU in software, like caches and things which will reduce it's heat dissipation, but execution speed will suffer.
Maximum junction temperature is typically around 110°C, so the device should operate normally up to that point. If you exceed that rating, it's likely to do bad things.
If you're worried about CPU cooling, there is an entire section in the datasheet about it, along with some simple calculations and tables for heat dissipation, thermal resistance of the case, etc.
As for the clock speed reported by your program, it probably measures the timing of a certain clock signal to get that info. The crystal oscillator's output (which clock signals are derived from) is a fixed frequency, and there's definately no way it's going to change according to CPU temperature.
Most likely your oscillator is about 49.9MHz or something, so depending on the way the program measures and reports whatever clock source, it may sometimes get 49MHz, sometimes get 50MHz.
Use a real frequency counter if you really want to remove all doubt.
