Your friend needs to be aware that to get a 'hot' holiday he'd need to go well south into Africa (e.g. The Gambia) or consider long-haul destinations (such as Australia). None of those are cheap (although The Gambia isn't mega-expensive) and they're probably unrealistic for just a 10-day break because of the time spent travelling. Further, such destinations aren't served directly from Luton.
The warmest places he can get to cheaply and quickly are in the Canary Islands. For example it's usually around 20C by day in January in Lanzarote:
http://www.holiday-weather.com/lanzarote/averages/january
As an example, he could fly out on Sunday 11/01 and back on Wednesday 21/01 for around £72 return with Ryanair:
http://www.ryanair.com/
Transfers shouldn't cost too much:
http://www.resorthoppa.com/airport-transfers/canary-islands/lanzarote-arrecife-airport-ace
and there are loads of cheap, but good hotels:
http://www.booking.com/region/es/lanzarote.en.html