An unfiltered, but heated, small tank is not a good place for a cory. Beside, they are schooling fish and should have at least one or two companions of their own kind.
An African Dwarf Frog would be good though. Click on the link in my signature for more information about them.
What is an ADF?
Also im not very learned when it comes to filters, in my coldwater tank i have a fluval one plus but it creates quite a current of water that it pushes out. Do all filters do this. From what i have read bettas dont take kindly to a strong current in the water, can you get other filters that dont push out water? stupid question I know.....
ADFs are African Dwarf Frogs. Very cute little guys
Most filters for larger aquariums have some way of adjusting the water flow to create less disturbance. In the kind of filter you'd buy for a 2.5 gallon tank (undergravel or those Penn Plax box-type filters) you can buy a valve for about $2 that would let you adjust the flow of the filter. These filters don't push out water, they push out bubbles after filtering the water.
With one betta and an ADF, you don't really need a filter, IMO. You could also try a betta and a few ghost shrimp if you don't want a frog.