I'd leave it out longer than a couple hours, as after that time it will still only be half way between fridge and room temp. I'd leave it out overnight and check viscosity in morning, if still thin then leave out tomorrow all day. For me when I did this I was scared but basically you want the buttermilk to rapidly go bad by encouraging the natural bacteria in to rapidly multiply. Go slow just allows a chance for airborne bacteria to gain the upper hand.
If you can't get it to be really ripe and viscous and decide to use it when thin, I'd use lots to help kick start the lactic bacteria into making acid for you when you make your presumably American style Neufchatel (low cal cream cheese).
Also, when making Neuf, don't forget every few hours to scrape the drier cheese off the cloth walls to allow the moister cheese access to drain, otherside it will form a low permeable layer and keep your middle Neuf too moist.