A cold boot is when you shut down the computer all the way down. A warm boot is when you just hit the restart button, the hardware never looses electrical power. On a cold boot, if I'm having an issue I will shut the power to the computer off and wait a few seconds then turn the power back on and boot the computer.
A flush is when you use either a malware or a performance tool to scan and clean the system. Examples would be Spybot or CCleaner. The Windows OS has never been very good at cleaning up after it's self. It leaves all kinds of files in the temp folder, taking up HDD space, and entries in the registry that are no longer needed. Plus historically has not been able to manage memory very well. So you have to go behind windows and clean up it's mess, just as you do kids.