Resistor for high power but low energy (pulsed operation)
@AndyAka got to me first on this part: this is a common issue, and many power resistors are specified for this.

What you need to do is get on the net and start slogging through resistor data sheets.  Start with power resistors, and possibly with ones that are rated for pulsed power.  You're looking for a chart in the data sheet that relates either average power to pulse time, or that gives you the energy of the allowable pulse vs. time.

Not every manufacturer will help you out with this, and it's not something that is put front and center in marketing material.  So you gotta dig.  And absolutely positively don't assume that once you choose a resistor you can just let your purchasing department buy any old resistor with the same size and power rating -- you'll need to specify that resistor.