Hi Dennis,
Autumn weather is at least better than spring but does gradually decline. Certainly not warm anymore, we've had to get the barbour jackets out already.
All of Bulgan province is really nice and not too far north so a bit warmer than elsewhere. Uugi lake is alright, lots of migrating birds at this time of year if you're an ornithologist but I wouldn't recommend swimming on the grounds that the shallow water is pretty muddy. Tsenkher is excellent, hot springs and big woods, high altitude so very cold at night though even in summer and I'd book your camp in advance as they might be closing about now. If you can, try and get the Duut Resort which is the best in the area by miles.
Orkhon and Khogno are ok and KharaKhorum - by the way, that's an interesting spelling you've got there, took me a few moments to get it - is worth a visit. I'm afraid I've never heard of Tal Beun. I checked with some of the guys I work with and we're not sure where it is. As far as we can tell it'll probably be a small soum between Orkhon and Kharakhorin city where the guide knows someone with a few horses to rent or maybe makes a commission for bringing tourists. I couldn't say anything else about it but I'm sure that some of the other forum contributors will know it.
This route doesn't get much outside of central Mongolia which means that apart from Tsenkher it won't be too cold up till October (5-15 celsius although Tsenkher will go below freezing at night). However, it will mean quite a bit of off road riding. This is not a big problem if you're guided but without good local knowledge leaves a high risk of getting lost in the middle of nowhere especially in Bulgan , Tsenkher, Ugii and Khogno.
Chris.