When you turn on amp it is fine, beautiful clean sound, as it gets hot, about 30 continous minutes becomes mare and more distorted untill the signal fades to almost nothing.

Battery is not the problem.
It could be transistors, IC, elco etc. It must be checked.
This electronic parts, could be almost breakdown. At the beginning of the device is turned on, it work fine, but after a while it became hot, then the value is changed, then the circuit was not working.
Can also occur on the DC input, the diode and the elco (D006,C019,C40,C41). View image.

See the full diagram here :
Boss MT 2 Metal Zone distortion pedal schematic
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Sounds like the switch is malfunctioning. First thing to do is get a can of Contact Cleaner. Spray it in the small space between the knob and the white dots, then turn it all the way - back and forth several times. If we're lucky, that will fix it. Good Luck

It sounds like there may be an issue with the power amp section of your amplifier. When the distortion gets deep and saturated, it could be drawing too much current and causing the amp to shut down to protect itself. This could be due to a number of reasons, including a faulty power amplifier IC, bad solder joints, or a power supply issue.
You mentioned that you suspect the IC may be getting hot. If that's the case, it's possible that it's overheating and shutting down the amp. You may want to try cooling the IC with a small fan or heatsink to see if that helps. If it does, you may need to replace the IC or look into other cooling solutions.
It's also possible that there are bad solder joints or other issues with the power amp section that are causing the problem. If you're comfortable with electronics repair, you may want to open up the amp and take a look inside to see if there are any obvious issues. Otherwise, it may be best to take the amp to a professional for repair.

You left off the one bit of info we need... however, make sure the volume control on the keyboard is around the halfway point... If it is way down, turn it up and reduce the channel volume knob some. Make sure the cable from the keyboard is an instrument rated interconnect and not one intended for speaker (usually marked as such). Make sure the keyboard AND this amp are powered from the SAME receptacle... even if you have to run an extension cord. Listen with headphones on your keyboard to make sure the sound is clean there.

try a differrent speaker of suitable wattage and ohmage (displayed with a number next to a ? symbol on the back of the speaker),

or

remove the original amp speaker and gently push in and out on it, checking for uneven resistance or scratching. the speaker should retract and return smoothly, without any scratchiness or uneven resistance from within, and if there is any of this scratchiness or uneven resistance from within, the speaker is likely damaged from too much wattage or distortion.

Realize that the number on the volume control is only relative... it means nothing regarding what the amp can produce. With a high level output guitar you can easily drive the amp into distortion at very low volume control level settings... what counts is the actual output sound volume and specifically the voltage output going to the speaker. Once the amp reaches saturation, any further input just pushes it into distortion or "flat topping".
An oscilloscope on the output will quickly show when amp starts to flat top.

Have you checked that it is not the amp that is the problem? This is a fairly common thing to have the amp heat up and the thermal protection shut it down partly. Since the bass drops, a loose connection or bad guitar cable can cause that. If the signal becomes capacitively coupled only the treble will come through and be very distorted. Try a new cable. For the guitar, open the electronics area and look for loose or broken wire.

CHECK VOLUME CONTROL BUTTON.

Wayne, There's a time to take the amp to a pro shop andf get it done right. It' saves time and headaches, and also keeps you from inadvertantly smoking other parts or yourself. Now is that time.

There are many components in the system. Electrolytic capacitors are most suspect. C49, C50, C45, C51

There are many others but these are top suspects. You MAY be able to detect a change by cooling these components with circuit cooler spray.

ALSO check the +/- 16 volt power sources in the unit.