for me it depends on which water change i'm doing .. if i'm doing the 25% change .. i usually fill up my 3 gallon bucket that i only use for my fish .. treat that with water conditioner and let it sit till the temperature of my betta's tank and the temperature in the bucket is the same (i have a magnetic in tank temperature thing which makes it easily removable .. looks like this http://www.petstrut.com/shop/shop_im...ct/JW21600.jpg
) .. and while that water is adjusting to room temperature .. i take out 25% of the water in my 3 betta tanks .. and then when the water is ready i dump the new water from the bucket in ^_^
when i'm doing 98% changes .. i'll take my betta out and put him in an hanging container (http://www.petsmart.com/product/inde...ductId=3523859
) with his old warm water and place the hanging container hanging inside the tank with my other betta (if you don't have another warm betta tank .. just keep him in a warmer spot in the house and cover the container he's in so he's not losing too much heat).. while i siphon all the water out to my 3g bucket (it takes 2 runs per each 5g tank) .. then water the lawn with that water .. then i'll fill up the bucket and treat it with water conditioner .. and then put that water in the tank
i try to get the running temperature of the tap water to be as close as i can to 80 .. by holding the thermometer under the running water till i get it to where i want .. to reduce waiting time
but that's just my scenario .. everyone has a different way .. do what you feel is most comfortable for you and your betta
in regards to the intake of your filter .. it would depend on how powerful it is ..
(mr. bubbles likes to sleep on the filter intake .. the first time he did this freaked me out cus i thought he got sucked up by it and was stuck .. but it wasn't that at all cus the moment i saw this i started to open his tank cover and he just swam away happily.. he just really likes laying on it @_@ .. crazy little guy.. but my filter is a mini whisper in tank filter and has strength settings and i have it on very very low setting so he probably thinks it's safe there .. and his fins have never been cut or torn by it .. so i didn't remove the filter) ..
if you find that he starts to avoid his usual hang out spots because u moved his filter there .. then maybe it's not a good idea .. but if you must put it there then maybe baffling your filter may also be a good idea just in case =D