Flyback transformer temperature rise - reasonable value
Is it normal for this size of core to get to those temperatures at
those powers? If not - What is causing the excessive heating?

That is a pretty reasonable temperature to run at. In fact I'd say it's probably running cool compared to most flyback designs. If you generally look at ferrite data sheets they state how much the temperature will rise under certain conditions. I've just answered this question on a similar subject and, I'll use some of that information: -

What the above is telling you is that if the peak flux density in the core is 100 mT and you are switching at 100 kHz, that core-set will dissipate 9.5 watts and rise in temperature by 100 °C. It's a recommended limit value so it's not advisable to run at this level (unless you know what you are doing).

However the transformer is getting quite hot (65-70degC) after some
time.

That's fine!