Luke warm water in a shower and tub

[Geofd]

Try to throttle down the cold going into the valve,and see what happens

 

[MrInfoPhilly]

If the bathroom sink water gets HOT., then its the Shower diverter...., pretty sure its a blockage where the water enters the diverter to be mixed., the inlets are TINY., Normally when you take the SHOWER TRIM off., you can see set screws that take a flat head screw driver, for both the hot and cold...

If its' no set screw., then replace the shower diverter.