Q: Can Rousing Voice give temp HPs after resting?

[keterys]

That point is moot. If five minutes pass without you doing anything particularly straining, you have effectively taken a short rest.

You could attempt that route, but a PC doesn't have to take a rest and could literally do a jumping jack once every five minutes to deny it so... changing the rules works, saying they effectively rested doesn't work by RAW (for example, for those of us who DM LFR sometimes)