Another option, pretty free, is to use METAR messages - list of all airports with their's lon/lat if freely available somewhere on the net. Also messages for given airport is easy to obtain.
I think this is a great idea and I hope this service can be implemented in the near future.
Actually I tried to log real live (so not by means of an internet service) temperature data using the FRWD B600 sports computer. Although the B600 did an excellent job logging GPS data and monitoring heart rate it had very poor temperature readings (probably due to heat of the batteries). So the temperature data was pretty worthless (about 10 degrees difference with the real temperature). Because temperature reading was the main reason I bought the device I returned it (thanks to the nice people at FRWD that wasn't any problem).
The option of logging tempeature data / weather conditions would be, in my personal opinion, a very nice addition to Run.GPS! I don't know any free service but if I find one I will let you guys know! :)
There are few options - most common one - get current weather conditions from nearby airport (METAR message http://en.wikipedia.org/wiki/METAR). Example for Warsaw's Okecie - http://www.checkwx.com/wxmain/code/EPWA
Weatherunderground provides XML API to access it's data (http://wiki.wunderground.com/index.php/API_-_XML), but I don't know how it applies to terms of use.
I was thinking something along the lines of HTC's Manila program which provides current weather conditions at preset upload intervals. I am assuming they get that info from a weather site of some form.
Do I understand you right that you would like to have a history of weather conditions for your trainings? Well there are some services that allow for embedding current weather information in Google Maps, but I have no knowledge if a service exists where you can access weather conditions directly.
Would it be possible for RunGPS to have a feature where it downloads local weather conditions, in particular, temperature and uses that in training recordings?