I just picked mine up yesterday after much internal debate. I would say it is not a run out and upgrade unless you were really unhappy with the iPad 2 screen (I always thought it was a great screen). The speed is marginally better (to be honest, I have not tested out all apps). It does get warm...big deal. Screen is nicer. Not that much of a game changer in the long run. I compared both screens side by side viewing web pages, photos and iBooks. It is definitely nicer, but the iPad 2 is still no slouch. I would say buy it if you are into using these things to their fullest extent. I use it every day for work and for play (I am an attorney and have essentially been able to make it a traveling law office without the bulk of a MacBook Pro). In terms of size, I put them face to face and you can hardly tell. I think the extra bulk is only noticeable when one picks it up and it feels slightly heavier than the iPad 2. For me, the weight is better which was one of the reasons why I preferred the feel of the iPad over the iPad 2.
I still feel a little conflicted with regards to the need to upgrade from the iPad 2, but since I have done it, I have not regretted it. Not regretting something is not an resounding "must buy" recommendation. Some of us are in a better position to by what is an incremental upgrade. They are treating the iPad and the iPhone like MacBooks with spec bumps. Not a reason to drop the cash on the incremental upgrades. This is weird since Apple moves these items and droves compared to the MacBooks. If the next iPhone retains the same design, then the fix is in. I love the design, but if we get a 4SS, that would go a long way to support the people that say that this new iPad is an iPad 2S and it was Apple's intention to do so all along to pull more dollars from us.