I don't know how much I would be worried about 10 degrees (I am assuming F and not C) if the pressure increase was way out of line then maybe I would be checking it, but a 10F is a small difference and depending on the accuracy of the sensor it could be well with in the margin of error. for example if the margin of error is 5F then one tire could be 110 and the other could read 100 and they could be the exact same and it is just reading off on each one or they could be different by up to 10 degrees and read the same. so with out knowing the accuracy and precision of the unit its hard to say if it is a concern or not.
now as for the others, before you start flipping weight around what is the total weight of the rv, and do you have between 10 to 15% of that weight on your hitch? that is more important thing for your set up. Also when was the last time the wheel Berrings were done. if the grease is a little lower/less clean in the front axel it will run hotter and that will transfer heat to the tires. my hubs are cold to the touch (well luke warm but, I over service mine by redoing the grease every 3rd year, we don't use the 5th much anymore, one 1000 mile trip per year type thing.) the next thing I would look at is, is your rv level when being towed. if its riding nose down then you can increase the friction on the front axel which could explain a difference in temp. that means you have to lift the front end till it is level. you can try moving the weight around, but I would set up the proper hitch weight first, you say it is 650lbs then general convention you should scall around 6500lbs for the total trailer weight, then I would make sure the hitch height is set so it rides level, then go from there if it isn't closer.