Convert 24VAC SCR Dimmed to LED
What is right with the circuit:
The &quot;power management&quot; section, while it will be wasteful of power because it uses linear regulators, may work if the regulators are adequately heat sunk.  U4 may be heating up for other reasons (see &quot;PWM Wave Generation, below).
What is wrong with the circuit:
Rectification and Filtration:
With a 3A average draw, each diode will dissipate up to 1.5W.  A 1N4007 is rated at 1W.  So -- they're inadequate.  You should always go conservative on power supply products, so they're inadequate twice.
24VAC works out to around 33V peak-peak.  Going into a bridge rectifier you'll get a voltage that peaks at the p-p voltage minus two diode drops -- so, around 31V maximum.  After correct (keep that word in mind) filtration, you should be able to get something that ripples between 31V maximum and maybe 27 or 28V minimum.  That's not going to support your 30-35V LED, especially if your 24VAC power dips below 24VAC.
This means that the whole approach is inadequate.
And did someone say &quot;filtration&quot;?  In order to ripple between 31V and 28V, you'd need a filter capacitance of \$8333\mu\mathrm F\$ -- \$10\mu\mathrm F\$ is only 833 times short of that.  Fortunately caps that big aren't horribly expensive (I just found a \$10000\mu \mathrm F\$ example on Newark for $19 in singles, and didn't look beyond that).  Unfortunately, it's not been designed in.
PWM Wave Generation:
Well, OK, a 555 circuit isn't inappropriate.  But it's sitting right next to a processor that's doing practically nothing -- so why bother?
(edit):  WHAT???  The 1N5348 is an 11V Zener diode -- that's going to be trying to pull the 12V line down to somewhere around 11V.  This may account for why U4 is getting hot -- it's probably getting hot, too.
I'm guessing that the original designer put it in as a cheapo regulator using a series resistor from +30V, then changed their minds.  You should be able to just take it out.
Constant supply to the LED
Yes, where is this section?
Temperature control of the LED
It's unknown what this is doing.  But if the LED is giving a simple voltage, and you're going with a 555 to control the PWM, why not use a comparator?
Output Power Control
Very questionable, but it may work.  I would have taken care to drive it from a CMOS version of the 555, and I would have called out one that has considerable output drive.  Or I would have used a gate driver.  I'm not sure if C2 is there for any purpose other than to fry the output transistors.
In general, it's better to use one suitable transistor than to try to parallel them.  Yes, if you just can't find suitable transistors, go ahead -- but 3A at 30V is not a big challenge.
What to do:
If chucking it and trying again is out of the question, the first thing you should do is try about 1000 times more capacitance at C1.  This will mean that you're actually supplying the rest of the circuit with sort-of DC.  Monitor the LED current carefully -- if it's supposed to be current-controlled, well, that's not what's happening here.  While you're at it, monitor the state of the 1N4007's carefully to, or just preemptively replace them with power Schottky diodes that are rated for 3W dissipation (but they only need to be rated for 80V or more -- the 1N4007 is overkill in that regard).
It is possible to do this, and to do it nicely -- an engineer used to working with switching supplies could probably even do it fairly cleanly.  But it would involve rectifying the 24VAC into DC, then using a boost converter up to 35 or 40V, then bucking that down again through the LEDs in a way that maintains a controlled current.  That's utterly beyond whoever did this for you.