Desire overheating

20 hours of charging really don't make a difference.  When it's full, it'll stop charging.

As for apps running in the backgound, that COULD be the problem.  If an app keeps using the CPU, the phone can get quite hot and drain the battery in 2 or 3 hours indeed.

Let's start by defining "hot".  The normal operating temperature would be anywhere between 20 and 40°C.  Coincidentally, 40°C is the point where "hot" turns into "painfully hot" for most people.  So ... can you still hold the phone in your hand?  If you can, it's not really out of it's normal operating range.

If you can still hold it, do the following :

Let the phone charge first, unplug it and leave it alone for half an hour or so. 
Then look at the battery use (Settings -> About phone -> Battery -> Battery use) and see what's been using the battery.  (in the battery use screen, you can use the menu button and click "refresh" to update if the info seems incorrect)
If the phone has been on standby for a while, the first 2 should be "Cell standby" and "Phone idle".  If any of your apps is on the top of that list, get rid of it.  If not, get rid of ALL of them and see if that improves matters. (no worries, you can easily re-download them at the Market.  They'll still be listed in the "downloads" tab)

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I must add that the first few charges on the Desire won't last long.  Mine also only managed 6 or 7 hours at first, but in the first 2 weeks I really noticed an improvement.  Android apparently needs some time to get used to how you use the phone, and will adjust itself to optimize battery life as it learns more. 
I had to go through this twice myself.  Mine felt hot at first.  When using it intensively it can still get hot, up to the point where it feels slightly uncomfortable.  But never painfully hot.

@ esSBee : I removed the topic you made about this, since there's no point in discussing the same problem in 2 different topics.

I went to carphone warehouse to get my HTC desire to which the bloke suggest that I rinsed the battery what was left of it then to put it on charge for 8 hours and to do this 5 times well he needs shooting because I done what he suggested I left my phone on charge last night at 10 got up for work this morning at 6 didn't use the phone till 7:10 used it to play music for 3hours at when I fished the battery was on red and I checked the temp it was a 39.1 I can see loads of people writing stuff about the battery comfortable or not it shouldn't be that warm the screen goes that hot I can't leave my finger on there for more than 3sec before it irritates me I'm very disappointed with this phone its speed is not what I expected very laggy slow having to press things 3 4 times sometimes to get a response having to faf around with sms alert putting a track in a surtain folder no no no not good. the loudness of the speaking is shocking and embarrasing and tinny everything seems an effort to do or a flipping task best feature the drop dwn task bar at the top part from that bit peed off with my choice of phone ill be sure to get rid of it soon I miss my blackberry bold but the app store was pants that's y the talk was all about androids are the upcoming big iPhone rival what aload of Tosh please let me know how u feel about ur HTC desire or what I have said. Thank you dp1273@hotmail.com

Hi esSBee no I admit I was not a happy chap and I took it out on my HTC lol thank-you for your advice and I will do as u suggested to wait and get a battery. Just does my head in because I know that HTC/androids have the potential to beat that iPhone its the 21st century I can't understand y there is still hardware and software problems with phones technology is moving very fast as we all no so I thank-you again and I really should have more patients but I'm human lol cheers

In standby, after a restart (thus ensuring no user apps are running) the phone should be cold. If it is warm then either 1. the battery is faulty and self-discharging 2. there is a phone hardware fault or 3. a previously installed rogue app is starting at boot and using excessive processor time.

Remove the chance of 3. by uninstalling any downloaded apps (or doing a system reset) and 2. by changing the battery, maybe by swapping with a friends temporarily. HTH

That depends.  If your app uses the CPU even when in the background (which means it's a rubbish and badly designed app really), then a taskkiller might be a good idea.  In all other cases I'd advise NOT to use a takkiller at all.

Sounds like you have a runaway app on there.

Download "Watchdog Lite" from the market.  Once it's installed, open it and go through the setup. 
During the setup, set it to "conservative".  That way it'll only alert you if an app starts using resources when it really shouldn't.  Uninstall that app and find a replacement.  If you can't uninstall it, a factory reset might be necessary.

I live in Cape Town and my Desire never gets warmer than 33 celcius. It generally operates between 25 & 35 degrees here. Winter or summer, not a single glitch.

HTC Desire, Redux 1.2, Oxygen HBOOT, S-OFF.