I have a Mitsubishi Lancer and in the summer or on hot days if the car has been sitting in the sun, the rev counter, speedometer and odometer do not go at all. As soon as the weather cools down they come back on again, sometimes when I am driving the car. Can anyone explain? Thanks.

What year is your lancer? Are the clocks electronic or cable driven. Usually the speedo/odometer(trip) is cable driven, and there can be various reasons it stops working. The symptoms can be similar in each case (does not move or bounces around erratically), the cable may have broken and simply needs replacing. (most likely)
Also the drive gear (plastic/nylon) normally attached to the gearbox or drive shaft could be worn out. Normally this it held in place by a bolt or screw that holds the gear in place by the use of a plate or bush. In this case loosen the tightening device... the gear should slide or twist out quite easily and replaced just as easily.
Lastly it may be your speedo clock itself. In this case I would suggest sending it in to a qualified Machie... simply because of the time and frustration it saves you.
Just out of interest do you stay in an area renowned for snow or icy weather. If so its always a good idea to let the vehicle warm up and run your radiator for a while before driving as cable and clock gears may freeze up due to condensation.

Also have you tried simply jiggling the reset button, sometimes this gets stuck and may cause similar problems (unlikely though)

As for the rev counter, most rev counters work electronically from the ignition distribution system (not too familiar with more modern systems) you may find that there is a general electronic fault in your system (Also the reason I asked if speedo electronic or not). This would also explain the dimming lights. Again not enough info on model so try disconnecting the electronics to the rev counter and see if this changes the condition of lights, and vice versa.

Again on this particular subject I would be venturing a guess, so any one out there who has good advice please I too would like to hear from you on this subject.