If the problems only occur after the system has warmed up and never occurs after you turn on a cold system (i.e. has been off for at least 30 minutes), the parts may be getting too hot and are failing.
Often this kind of problem is related to poor air-flow through the PC. Desktops usually have between 3 and 5 fans. If any fan fails, runs slowly, or if the vents are blocked, internal high temperatures can cause all sorts of odd behavior and BSoD messages.
While the system is powered on, put you hand near the exhaust fans at the back and confirm you feel a warm airflow. If there is no airflow or it is very hot, it's a good bet you have fan problems. Also check the inlets and be sure they are clear of dust and debris. If you have pets, check if fur is blocking the inlet vents.
If you are comfortable opening your PC, turn off the computer and open it up. With the insides in good view, re-apply power and turn it back on. Check that each fan is working properly and they are not clogged with dust.
Be sure to check the CPU fan and the fan inside the power supply. Also many video adapters have their own small fan. Replace any slowly turning or defective fans. Also be sure no cables are too close to the fan blades, as they can limit airflow, or worse - stop the fan if they hit the blades.
Check if the processor heat sink/fan assembly is properly attached to the processor chip. It should not be loose and should be clamped tightly to the the processor.
If the fans are all working and airflow is good, you may have a defective CPU, memory or other hardware component.