The chances are you won't be able to use the old heatsink.

intels run cooler than AMD chips, but the i7 is a big jump up from the i3.

Is it the stock cooler (as in the one intel shipped) for the i3?

My i7 4778k gets 70°C under load and I have a pretty big aftermarket cooler on it.
I recommend getting one anyway if it was only for reducing the noiselevel.

I watercooled mine. No worries. :P

But yeah, you should at the very least try to get the stock heatsink for it.

Cooler Master Hyper 212 EVO
gl!

The i7 will produce more heat, however that doesn't mean the old heatsink won't work (as long as you're not overclocking).

I'd try it and watch your temps with something like Core Temp You want to make sure it stays below 90C under load (you can run something like Prime95 to keep it under load while checking the temps).

And as a probably somewhat redundant suggestion, make sure you get some decent thermal grease, as some brands seem to perform much better than others -- I've usually had good results from the Cooler Master and Arctic stuff.

Bloody good cooler!

I installed one a while ago, because I OC anything that can be OC`d.
It kind of shocked me how cool it keeps things :D

Only problem, it is rather large, but it does the job.
Oh, not exactly quiet either. Not loud, but... Apparently there are quieters ones out there at similar prices though.

It might not be 100% necessary. But having it could improve the life expectancy of your new chip. Which is something worth doing, right?

Its big. I've got one in my case. It only just fits. The side panel actually touches the top of the cooler.

That's rather compact for a tower cooler. Try this one on for size...

Saw a fan linked on PCMR subreddit other week, looked like the size of innards of a washing machine, but can I hell as like find it... Ah well.

I HIGHLY recommend never using the stock heatsink/fan. It doesn't need to be a Noctua, but I recommend getting a 3rd party heatsink. 1st party ones are usually not that great/efficient. See logicalincrements.com for one that matches your budget.

I would splurge as much as you can for the best heatsink you can get for the i7. I would recommend Noctura because IF you intend no upgrades for several years, that brand will probably last you a long while. Pricey they are but my i7 5930k is at about 90 degrees Farenheight idle with the NH-D15S ($99). The last heatsink I had was for a i7 920 and was also a Noctura but the motherboard started dieong before the CPU fan