To save on heating costs, best way to do it is to make a drip system running off a main sump. That way you provide your betta with cycled, heated water on a constant basis.
Heaps of DIY videos on Youtube showing you how it's done. It looks complicated but it's mostly just finding the right parts and sealing it correctly.
It is rare for there to be an outbreak of disease such as velvet or columnaris in any tank unless something has either not be quarantined properly, there has been an extreme temperature fluctuation, or your water parameters are not ideal.
If one fish does get sick though, treat the WHOLE system not just the one fish as this is where you will lose them. Because the water is shared, every single betta has been potentially exposed, so you have to treat them all.