How badly do you want to go to the beach? Personally I'd skip the beach given your interests.
I would probably do a couple of days BKK to get used to the climate and time zone.
Then I'd say head to Chiang Mai for a few days. Lots of old temples in the city, mountains nearby and some other nice sights. You can also include Chiang Rai and other places around the north.
There used to be direct flights between CNX and REP (IIRC). But I am not seeing any at the moment.
If you are interested in history I would spend more than 2 days in Siem Reap. There are some outlying temples that are not as frequently visited that are worth going to but they take some time to get to.
While you are in Cambodia you might consider spending a couple of days in Phnom Penh.
Then finish the trip with a couple more days in and around BKK.