Meaning of temperature coefficient for resistors
The temperature coefficient specification ostensibly provides a limit for the change in the resistance of a resistor from its nominal value at temperature \$T_0\$ to another temperature T. In fact it's usually defined using a box method at temperature extremes and does not really guarantee the slope of the temperature-resistance curve as you might assume. 

Ideally, a maximum temperature coefficient of, say, 10ppm/°C would mean that if our 1.00K resistor measures 1.0015K at 25°C and the temperature changes to 35°C then the value should somewhere between:

\$1.0015K + 1.0015K (35°C - 25°C) 10^6 \cdot 10ppm/°C \$

and 

\$1.0015K - 1.0015K (35°C - 25°C) 10^6 \cdot 10ppm/°C\$

Or 1001.5\$\Omega\$ +/- 0.1005\$\Omega\$

It doesn't matter why the temperature changes- ambient, self heating, nearby components, or some combination. 

If you are trying to measure the actual temperature coefficient of a resistor, you can measure the resistance at two widely separated temperatures, using low enough current that self-heating is minimal (note that it cancels out to a first order if you allow it to settle out- also pulsed current can be used and the measurement made before the temperature changes much) and calculate the tempco as: 

Temperature coefficient = \$\frac{R_X - R_0}{R_0(T_X-T_0)}\cdot 10^6 ppm/°C\$

If the tempco is large you might want to use the average resistance rather than \$R_0\$, but it shouldn't matter much in most cases. 

Edit: Regarding the situation you mention - 0.2% change for a change in power dissipation of about 100mW.. you need a better resistor and probably a larger one that won't heat as much for a given dissipation. 

Consider a 1206 249 ohm Susumu resistor. P/N: RG3216P-2490-B-T1. Tempco is +/-25ppm/°C, it will increase by 15-30°C at 20mA depending on layout (see the link). That should represent a change in resistance of about 375-750ppm or maybe 3-5x better than you are measuring. If you need even higher accuracy, you could use a bigger resistor, several smaller ones distributed with copper around, or use a smaller value resistor and amplify the signal so it doesn't get as hot.  

You could also use a Z-foil style resistor such as Y1630250R000T9R that has only 0.2ppm/K tempco, but they are pretty expensive (>$10 each).