While we do not have enough information to zero in on your problem you can begin by checking to make sure that there is no obstruction of air vents on the unit. Sometimes something as simple as having the unit setting on a carpet can block air passages. The second thing to check is if the fans are working properly. There is likely a power supply fan and there may be a CPU fan. If the fans are working properly then you may have a component that has gone thermally intermittent. This can be very difficult to find. When I had this problem I could sometimes locate it by waiting for the unit to fail and then spraying different areas of the circuit with circuit coolant to see if I could make the unit work again. I would repeat this until I could isolate a very small section of the circuit that was sensitive to the coolant. Eventually I would isolate the one component where the application of heat would cause a failure and the application of coolant would cause the unit to start working again. Good luck and keep us posted.
looks like you have the red ring of death. my old xbox had the same thing. I used the two cures that can be found on youtube. 1st is the main heat sink, carefully remove it and reapply heat sink compound. rap in blanket and reset compound. 2 fix rap four sets of two pennies in electrical tape apply to the four outer chips with heat sink compound and bake in. both worked for me. for full directions go to youtube and look for xbox fixes or the red ring of death. I hope this helps you out.
