Thank you! So, following your calculation, what really matters are the RDS(ON) and RJA values. That means that with this guy we would get to cca. 278 oC above ambient at 8A and VGS 5V. I hope I didn't make a mistake... 
That seems too much, but now at least I know what to look for when choosing a MOSFET. Thank you again, Mike, for clearing things up!