Typical dissipation constant of average thermistor?
If you look at the datasheet you should find a number. If no datasheet you can 'guess' by comparing a similar size and package part (confirm the lead material is the same to be closer to the truth).  

You should also look deeper and find the conditions under which the dissipation factor is measured (typically in an application note or manual, rather than in each individual datasheet). Ideally something like 'still air, 1°C above ambient, and 50mm leads'. Not so ideally, something like silicone oil flowing at 1m/s (well that would be a bit extreme, but you get the idea). The exact same part immersed in oil or with forced convection will have a very different factor from that in still air. 

Here is is a typical thermistor datasheet specification: 



Note, for example, the conditions under which they measure the 'response time'.

If you use a series resistor to a fixed voltage source you would normally  pick that resistance to be close to the normal operating temperature (to maximize the resolution, which will fall off dramatically at higher and lower temperatures for common NTC thermistor types which change around 5%/°C). Of course that also maximizes the self-heating at that point since the thermistor resistance matches the Thevenin-equivalent source resistance. For example, a 10K thermistor in series with 10K 1% will have a power dissipation maxima at the temperature where it is 10K, and it will be ~0.6mW with a 5V supply.