This is serious power for a switch mode DIY solution. I would suggest not to waste money & effort in designing it. You can use something like this
http://export.farnell.com/emerson-network-power/lcm600q-t/psu-ac-dc-600w-single-output/dp/2115741 if you absolutely want regulated voltage (Datasheet:
http://www.farnell.com/datasheets/1624416.pdf). If you really want to design something, try an unregulated linear PSU as others suggested. If you want to regulate it, you should consider some (at least 3-4) transistors in parallel.
Very quickly, to calculate thermal demands you go something like this:
Ok, I have a, say, 230/24V transformer. Worst case is 230 +10% so 24 + 10% = 26,4VACrms. That is (26,4 * 1,41) - 1,4 = 35,8VDC (worst case). Your regulator will output 24VDC so you're going to have 11,8VDC voltage drop. The maximum worst case power dissipation therefore will be 11,8V * 20A = 236W. If you use, say 8 transistors, each one is going to dissipate 236/8 = 29,5W.
If I use TO247 transistors like these
http://www.st.com/web/en/resource/technical/document/datasheet/CD00001165.pdf they typically will have Rjc = 1C/W. In this I have to add, say, Rch = 0,2C/W typically. So we have so far thermal resistance from junction to case and from case to heatsink is 1,2C/W. So, I'm going to have 29.5*1,2 = 35,4C
above ambient temperature for my transistors. But I haven't calculated the resistance from heatsink to ambient. If I use a 2 heatsinks like this
http://export.farnell.com/fischer-elektronik/la-6-150-12v/heat-sink-fan-cooled-12v/dp/1222507 I'm going to have (236/2) *0,175C/W = 20,6C in every heatsink
above ambient. So, total increase in temperature should be no more than 35,4 + 20,6 = 56C. For the specified transistors I see that the maximum temp. is 150C so the maximum ambient temperature my circuit could work safelly is 150C - 56C = 94C Which I guess is fine. But also there is something else. You have to derate the maximum power of the transistor as temp. goes higher. This is usually specified in the datasheet. For example, if my transistor has maximum power 150W with a power derate of 1,5W/C above 25C that means the maximum power for this transistor at 100C whould be 150 - ((100 - 25)* 1,5) = 37,5W. So, in our example, if my transistors have characteristics like this, 150W max., 1,5W/C that means 150 - ((Ttr - 25) * 1,5) = 29,5W -> Ttr = 105.3C and since this includes the 56C then the maximum ambient temperature will be 105,3 - 56 = 49,3C.
From the above you can see that 2 heatsinks like that will cost about $130. Plus $24 for transistors plus maybe $100 for transformer you're easily above $300 for single quantities. The EMERSON NETWORK POWER - LCM600Q I suggested above goes for about the same price.
Hope that helped.