Good evening!
I am new user of Ubuntu and Linux at all! Few days ago I have installed last Ubuntu Mate LTS on my laptop and I determined that after hour or few of work my laptop becomes hot and works slower and slower.
What I have to do to solve it?
What kind of information about my laptop should I provide to you to solve this problem?
Sorry for my English! It is not native language for me! 
I recommend that you use UM 16.04.x LTS.
There are serious issues with 18.04. It hogs resources, and has the stability, at best, of a beta, and sometimes, of an alpha software.
Thanks to fast reply! I will try previous version! Will it solve my problems with overheating?
Hallo Stanislavs Kapustins
I do not know how old or new your computer is, however, Ubuntu-Mate is sometimes said to be a distro that does not require too many system resources - that is, it will run well on older computers. This is not really true - that is not the main focus of Ubuntu-Mate. If the Ubuntu-Mate versions you try seem to be too much for your computer, you might have more sucess with “MX Linux”:
https://mxlinux.org/
If MX Linux does not run well on your computer, try to talk to someone at a nearby “LUG - Linux User Group” meeting. Your computer might be the problem.
Ubuntu-Mate is a very “easy-to-get-to-know” distribution and a very good place to start your journey with desktop GNU/Linux. I hope 16.04 works for you. 
If you want more help you could let us know which CPU your computer has, and also how much RAM.
For me, 18.04 is super stable. It includes myself, other users and tens of computer that are used in my classrooms.
Can you detail what is buggy? Do you have some pointers to bug reports?
The problem is that you are basically spreading wrong information and sending new users to wrong directions.
You should ignore this advice and detail what is slow.
If your laptop heats, it means that your CPU is busy. What is the process showing up in the monitor or htop ?
Your problem may not be related to Mate, or it could be just one component that you can disable or fix.
I have a long list of issues. Ranging from crontab not working to Samba mounts becoming un-writable mysteriously, to browsers maxing out the CPU (i7 4th gen.) routinely, to fingerprint login not working. I have submitted many bug reports.
It is not false information. It may be an anomaly but it is a real experience. I am not a Linux newbie. I understand I have to do some manual tinkering. I have done many hours of searching, tinkering and requesting support. Just freakish bad luck? Could be.
What video driver are you using?
I’m not sure the question was addressed to me, but this system has only the onboard Intel GPU. On my other system the Nvidia driver is running. Both systems generally make heavier use of the CPU than Windows. VLC can play high bit rate video without stressing the CPU, but video playing inside the browser causes a range of behavior. In some cases the CPU usage is kinda like VLC, but in other cases it maxes out the CPU. If a 1080p 60fps video is playing in Youtube, it takes close to 100% of the CPU—forget about multitasking.
With Windows I almost never push the same CPU past 25% or so. The CPU just shrugs off my work loads like its peanuts, and I am multitasking constantly and sometimes pretty heavily. Video file rendering is the only thing that takes more than 50% of CPU. So, for the first time in my long experience with Linux it’s being beaten by Windows in resource economy.