You'll probably see some ill effects in the longer term at that temperature. Most bettas in stores are only there temporarily, not to mention that they lose of lot of them while they're there.

I've had a heater break on a betta tank before, and even though the room was warm, she still got whitespot in the few days it took for me to source a new one. Better to get a small heater than to risk it - he'll probably be more active too.

 

A significant reason that Bettas become sick in those small cups at the Pet store is due to the stress of temperature.
Bettas come from warm tropical climates in Thailand that stay very consistent throughout the year. The recommended temperature for Bettas is 78-80 degrees- a small window of temperature variation because that is what they are accustomed to.

Temperature stress lowers the immunity of fish and, with Bettas in particular, increases the probability they will succumb to Columnaris.

 

Years ago I kept betta in 1 gal bowl while waiting to get a ten gal tank set up. Summertime temps were fine, in winter I kept the bowl warm enough by putting on top of my fridge- the heat vent happened to be in the ceiling right above the fridge it was a very warm space. At night I would wrap the bowl in a wool scarf. My betta survived, but I wouldn't keep one like that again- he was much more active and appeared happier when finally moved into the proper tank with a heater. He also did not live long- under a year- and I think part of the reason is he spent months in the bowl.

Seventy is cool for a betta- i would make sure his home is at least 78. There are mini heaters made for tiny tanks, you might find one that works in the bowl.

 

Stores keep them in cups because they don't die in 3 days in the conditions like most other fish would. That doesn't make it ok! Bettas are tropical fish who should be kept in decent sized tank with a heater and (low/baffled flow) filter or live plants to keep ammonia in check. Bettas should be kept at bare minimum 76F, and can go up to 82F, 78F being the 'sweet spot' most proper owners keep them.
They will be more comfortable/happier, more active, and interactive when kept at a proper warm temp.
When you get a heater, don't get a pre-set or always on style-those are most prone to frying and boiling fish, some brands paint will peel off the heater.. no good. Get an adjustable heater-the most common recommended by betta owners is Hydro Theo, 25 watt should be plenty for your small tank.
https://smile.amazon.com/Hydor-Subm...6GR&keywords=hydro+theo+heater&qid=1548017854&sprefix=hydro+theo,aps,132&sr=8-1