2005 Ford KA car looses power after 20 of driving ans wont move til cool

My car lately has had trouble turning over in the morning. So I got the battery checked over and the said that it was fine.
Then, this week my car has broken down 3 times. Each time the breakdown guy has been totally bamboozled as to what the problem is, so I took it to the garage and they can find anything either, so here goes..................
When I drive for around 20 mins and I reduce my speed for junctions ect the car has an inability to regain spead so I have to pull over (the engine as far as I recall does not cut out)
Once I try to pull away it feels as though the hand brake is still on.
Then if leave the car for 40 mins or so the car cools down and everything is ok.
The car goes into the garage tomorrow so I don’t want to spend more money on process in guess work its already had the clutch checked and a diagnostic dome so any help would be really appreciated.