Usually MD simulations start with crystal structure, which is generated at much lower temperatures, or from NMR structure which is experimentally generated at around 300 K. When you solvate any of these structures in water + salts, it is recommended to increase temperature slowly from low temperatures 10-100 K (depending if it is crystal or nmr structure) to 300 K (desired temperature) restraining/constraining heavy atom positions of the protein at their initial structure. You can in principle continue increasing temperature using restraints/constraints slowly up to 500 K or sometimes even higher.

If you want to increase the temperature above 300 K (or initially even up to 300 K if you start from crystal structure) without any restraints/constraints, then your protein may 'blow up', first because the volume of protein in crystal structure is not the same as in solution at 500 K; secondly there could also be numerical instability due to bad contacts between atoms which increases the forces between them. Therefore, it is recommended, to avoid any instability, to increase temperature slowly up to the desired temperature using restraints or constraints on heavy atoms.

The increase/decrease of temperature is done using special protocols, called simulation annealing, below you have a link how to write a protocol in gromacs:

http://cftcc.iccas.ac.cn/upload/doc/gmx/html/online/mdp_opt.html#sa

It depends on what ensemble you are using, but often NPT breaks down at high temperature. Using NVT is much more stable, but one needs to simulate using the relevant ensemble, not one that "just works." Reducing the timestep is also generally necessary when simulating at high temperature.

If you are using the NPT ensemble the reason for "blowing up" is simply that your system evaporates. As Justin said, the NVT ensemble is more suitable for higher temperatures, however if you equillibrate your simulation at 300K and then got to 500 with NVT your density is not the correct one. You would have to find a pressure a bit above the vapor pressure of your system at 500K to keep it liquid in a NPT run and use a smaller timestep due to the possible fluctuations...