The first "death by heath" was covered by Apple warranty, the second was not. I have therefore picked up a new power supply from eBay and replaced it manually. The Time Capsule was resurrected but it kept overheating and it was just a matter of time before it was going to give up again. Someone actually made a business out of fixing Time Capsules :) A wonderful wealth of info can be found on this site: http://www.fackrell.me.uk/
I almost gave up on Time Capsules but I could not find an alternative that I liked apart from the new model so I looked into a way to better cool it. There are many way to do this, but all required me to drill, cut and solder.
Being the creative (read lazy and with a limited tool set) person I am, I found this USB LED Cooling Pad on eBay for next to nothing! :)
The cooling pad is perfect. It looks great and delivers exactly what the doctor prescribed, a steady flow of air to keep the Time Capsule alive. Here it how it looks like action now.
The fan is not completely silent, but it is not loud enough to be a nuance. It cools the Time Capsule really well. The bottom of the Time Capsule used to be very hot and that's even after removing the plastic bottom cover from it and adding little rubber legs to keep a gap for heat dispersing. The nice thing is that the fan is USB covered and can be plugged into the back of the Time Capsule.
I have been using the USB at the back of the Time Capsule to power Google Chromecast and since I have run out of all available power outlets in the area and wanted to avoid running more extension cords, I have picked up this Cute USB Mini 2-Port USB 2.0 Hub Splitter. It is reliable and fits perfectly.
I hope this post will help someone time and money! :)