Stellar flares rarely go directly toward a particular planet even when they occur, which isn't that often, and the normal nasty effect takes days to get there (unlike the light which only takes minutes). In 3.5 hours, it won't make a difference, so flares are the least of their worries. 3.5 hours is a narrow window - not as bad as checking out the natives in The Paradise Syndrome when they had to deflect that moon-sized asteroid - but even there he may have needed to confirm the natives were too primitive to notice their space shenanigans lest they violate the prime directive. In All Our Yesterdays, it might be highly useful to know what could make a whole population disappear. It could happen to you, too, if it's another unknown danger sneaking around the galaxy, so best to find out if you can. You have 3+ hours. For a quick look, that's not so bad. And he wasn't risking the ship - just 3 guys. Risk IS their business. I'm more amazed that Kirk and the Enterprise is always showing up in these incredibly tight situations in the nick of time, right at that moment of crisis, and after crossing light years of space, it's always so improbable. At least there, they went to see the nova, probably, and when they noticed the population was gone - well - that's a hell of a thing. We got 3+ hours and a safety margin. Let's go see. YMMV, of course, but of all the things Kirk has done, this one didn't rank too high on my WTF was he thinking moments.