Why is 10W resistor getting hot with only 6.5W running through it?

First let's do a quick number crunch:

6.528W/10W = 65% (of 10W)

Referring to the datasheet:

There is about a 165C rise in temp. Do not touch!.

As for "Is it a safe temperature for the resistor?", refer to the next figure:

I'll admit that the Derating Curve Graph kinda hurts my head. But, if you follow the 10W curve over to 25C (about room temperautre), the resistor should be able to handle 100% of it's rated power. Note that I'm only assuming the ambient temperature is 25C! If you have it lying on a brick, it should be okay. It appears that the resistor can handle up to about 115C ambient temp @ 65% load. But that would be pushing it to the max.

This is normal behavior for a power resistor of the size you are using. Just because it is running at 50% of its rating doesn't mean it will run cool. I looked at the data sheet for a similarly sized 10 watt resistor. It had a curve showing temperature rise versus percentage of rated load. For 50% (5 watts), the temperature rise is 125C which is greater than boiling water.

You are pushing 6W to the resistor. That means 6J of heat per second.

Using calorimetric equation Q=c.m.(T2-T1), where Q is total heat, c is specific heat capacity, m is mass and T are temperatures, one can derive P=dQ/dt=c.dT/dt.

If you use your values, you can see that the resistor's temperature rises according to P/(c.m). Thanks to its small weight, the rise in temperature is really fast.

There is also counter-process: heat dissipation. The higher difference T-Ta, where T is resistor temperature and Ta is ambient temperature, the higher heat dissipation. There are more variables to rule the dissipation and the temperature: Heat capacity of the heatsink (air), mass flow of the air, etc.

Regarding your question:

• Yes, it is normal and it is caused by power to weight ratio.
• If insufficiently cooled, it will get really hot.
• If it will be resting on a brick, there is no fire hazzard. If you put it between two bricks and seal it, it can melt itself and burn. If left with flamable pars, there is fire hazzard.
  Personally, I would add cooling to it, small aluminium radiator shall dissipate 10 W easilly (Foolproof roundup).