As long as you have a quality power supply, and more importantly it's rated for the correct Volts for your strip, some strips are 5v some are 12v. You should be fine.
Also make sure it's not just a bad strip. But the LEDs will get warm, not hot enough to burn you, but yes they can heat up. That's why you see all these house light LED replacements with these crazy heat-seeks on them. Not tungsten bulb hot, but they can heat up.
Nothing to worry about.... Till you see smoke. Most strips will fry before they get hot enough to burn you.