I have had my 95 Dodge Neon for over 5 years now with no problems, other
than those I knew about when I bought it.  
  When I bought it the engine light was on and it had been checked and
they could not find anything wrong with it.  It started coming on when
they previous owner replaced the engine.  Sometimes the light goes off all
on its own and then a few days later it will come back on.  
  The lights behind the A/C controls are usually off but on a good day
those lights will decide to come on.  
  The lights on the gear shift were up until recently usually on.  Now
they are usually off whenever I turn on the lights.  
  Since I purchased the car occasionaly the left turn signal light in my
car would come on as a constant light, but if I jiggled the turn signal up
a bit it would turn off.  After I rotated my tires using my left turn
signal caused my caution lights to come on.  My dashboard said that it was
a regular left signal only except when I would brake as far as my dashboard
lights were concerend my left turnsignal was a constant light, not a
flashing signal, and no matter how much I messed with the signal it
wouldn't fix itself.  After a day this problem suddenly fixed itself.  
  This leads me to my current problem.  After about 45minutes of driving
both highway and in town my engine heat needle went all the way up to the
H (past the mark) and the dashboard started beeping.  As soon as I turned
off my headlights the alarm stopped.  I turned the car off and when i
turned it back on after 10minutes or so the needle was at the 2/3rds
however when I turned on the lights it immediately shot up past the H
again.  Now the lights don't seem to make a difference and its not doing
that again.  There is no leaking so no hose has broken, the hood doesn't
feel hot and its definately not smokeing.  Coolant is filled, and just had
an oil chnage.  I can get the needle to go back down if I turn on my heat,
but I am not sure if I were to leave it running for longer if the needle
would just go to the top again.  While sitting still and without any
inside fans on the car going after around 20minutes the needle went past
the H again, sat there for a little while and suddenly started dropping.
I have no idea what is going on.  I understand a bit about cars but this
is way past me.  I recently moved as well so I don't know what shop to
take it to in the area.
Any suggestions?  Sorry such a long post but I am secretly hoping its an
electrical problem and the engine isn't overheating.  Or its just
something super cheap.
Thank you!
~Andrea