I've flown along that trans-Sahara route a many many times (primarily between London and Accra / Ghana, and other West African destinations, in B737-700 and B757-200) that said, there's no radar coverage over vast swathes of the Sahara Desert and therein ATC uses what's known as a 'procedural service' (i.e. using only radio position reports), and that radio position reporting was often via HF and seemingly to some bloke sitting in a tin shack in Bamako and whom sounded like he was speaking into a tin bucket (and all he ever wanted to know was your aircraft type and registration, so that they could send your airline the bill for their 'service')
Also at this time of year, the ITCZ can top out out +50 thousand feet, therein allowing Cb's to grow to huge size... and trust me when I say that Cb's over the Sahara can match anything that the mid-west USA has to offer in its tornado season.
You can be at +FL370 and yet still looking up to see the the top of those clouds as they stretch high above you, even when you're +100 Nm away from them. I've also regularly witnessed lightening jumping the gaps between those Cb's, and you can sometimes even smell the electrical ozone in the air. Those Cb's can be true monsters and well worthy of giving much respect and distance !
Accordingly it's also not uncommon to be hundreds of miles off track (as indeed will be other aircraft too) whilst dodging around lines of massive thunderstorms. However, given the difficulty of getting an ATC 'Clearance' (i.e. to diverge away from the airway), rather than dive through a Cb, you just did whatever was necessary to avoid it (just as indeed would everybody else). At those times, TCAS and 126.9 (IFBP) are invaluable aids for Situational Awareness!
TIA !