Its not necessary to provide extra heat in feeding tubs. Not sure what you were asking with the second question... were you asking what size rat/mouse or were you asking what size tub?
Here's a recent post on the topic of feeding containers that covered pretty well everything, I couldn't have said it better myself...
Originally posted by Big Mike
This has been debated many times. While some people think that snakes will "learn" that food is comming in every time the enclosure is opened...if you feed in the enclosure...other people think that taking your snake out of it's enclosure to put into a feeding enclosure...could trigger a feeding response.
Here is what I think. If you alway make sure that you don't smell like food then reaching into the snakes's enclosure should not trigger a feeding response.
If you think that by feeding in the enclosure, you are conditioning it to bite anything that comes in. Think about it this way...by that logic you would also be conditioning it think of food every time you took it out. Then you are holding a snake that thinks it's dinner time. Also, you should not move a snake that has just eaten, to prevent a chance of regurgitation. So what do you do after it has eaten?
If however you keep your snake on a loose substrate that would be harfull if injested...feeding in a seperate container may be the better option.
For my snakes that are on loose substrate, I put a small feeding container right into their enclosure. This fay they can go in there to eat and can come out on their own.