Temperature Dependent Frequency of Relaxation Oscillator
The saturation voltage of the comparator is one obvious contributor. The comparator will also have some offset voltage shift with temperature, the bias current will change, and the response time will change. 



If I was going to make a wild-a** guess I would say it's probably the response time, which will be probably several microseconds with a ramping input (note that the time is specified as 1.3usec typical, only at 25°C, and with an overdrive of 100mV) -- so a change of only maybe +/-100ns will account for your measured change. 

The output voltage could too, but only with a rather large change in temperature (which you did not deign to mention- it's kind of important). 



What you can do to make it better next time- control the voltage that sets the thresholds and the integration current better, pick a comparator that is much faster than the required switching time and that has very good DC stability. 

As an out-of-the box suggestion, you can get much better performance even with a crap circuit by making two circuits or switching inputs so that you measure your unknown capacitance and a reference NP0 capacitor. This will also cancel out some other sources of error such as resistor drift (use 5% resistors if you want), and even a certain amount of power supply noise. That's what I would consider if I was making a whole bunch of them.