I had a similar problem with my shower when I first moved in. I think that it will most likely be the thermostat inside the shower that is either set too low or has become unresponsive due to lime scale build up. If you undo the cover at the centre of the shower unit you will find a large screw. If you undo that you will see there is a hole of about 5 mm diameter. You will need a very long and narrow flat blade screw driver to reach the thermostat unit. Adjust the thermostat until the water mixes to be slightly hotter than you require.
Limescale build is another problem, to solve this one I removed one of the output covers of the shower and filled it up with cillit bang and left for a few moments and then flushed the water through.
You can test that you are getting hot water to the shower by turning the shower to about 9pm so its running with majority cold. If you then feel each of the feed pipes you should be able to feel what one is the hot. Mine is too hot to hold for any length of time.
I have a user diagram for the shower at home and should you require that to gain access to the thermostat then let me know and I will post it.
Hope that all helps.
All the best
6 / 97.