Possible Short?

I have recently acquired a 1971 DAX 70 it has less than 400 miles on it and is in pretty good shape. When I removed the original battery and installed a new one the rectifier got very hot I am assuming that there is a short causing this. What may be the possible causes of this problem? After cleaning the carb the bike runs pretty well and with the old battery which is dead the brake light and horn works when the bike is running. Any suggestions would be appreciated.

It's normal that the selenium rectifier warms up.
But it's hard to say if it's too hot or not in your case.

I'd recommend to (correctly!) fit a new style rectifier, as the orange plates aren't very reliable, certainly not after all thise years.
Honda has got new style 6v rectiefiers as a spare part.
And... as you said yourself, check the wiring for any breaks are wrong connections (to the mass for example) as this can cause overheathing, and damage to the battery.

I did post the electrics scheme on this forum somewhere.

PS: it's normal that the brake light & horn only work with a battery fitted.

Thanks for the info the rectifier got hot enough that I actually smelled it before I found how hot it had gotten in the couple of minutes I had the battery installed. I will have to pick up a replacement to convert it I was hoping to keep the bike all original but also want it to be reliable. Once I get it cleaned up and polish the chrome I will have to post some photos it could end up being the nicest bike in my small collection. Thanks again for the help.