I have a blower motor which runs on 12v with 25min running 5min rest rating. I want to run it at 5v-1amp (significantly lower speed) for at-least 14hour continuously. Will that hurt burn the motor? The reason I think it may work is because I am running almost at the third of the rated voltage.
Assuming the limitation is power/heat buildup...
The power dissipated in the motor winding is a square function... if you decrease the voltage by 50% (and therefore the current) you have decreased the power by a factor of 4... down to 25% of its original value. Any motor rated to run for 25min "ON" time, and at 80% duty cycle, will surely have no problem running continuously at 5 volts... if indeed it will run at all.
Just understand that you don't have a say over how much current the motor will try to draw. If it required 25 Amps at 12V, that's the equivalent of 2.083 Ohms in the windings. At 5 Volts and 2.08 Ohms, it's still going to require around 2.4 Amps. (although the load of the fan/blower will be quite a less at the lower voltage & speed, offsetting some of the Current)
As long as the motor will run at 5 Volts, and it doesn't try to overload your 5V power source, it should be fine.