Pull the gauge out and use a jumper wire to ground it somewhere. If this
works, you have a bad ground. If not, replace the gauge.

Have you considered that the temp guage itself is toast?

You are looking at the complicated stuff like the steering wheel play -- or
the wrong stuff in the case of the t-stat -- but ignoring the actual
symptom.

There may be two temp sending units on the motor, one that feeds the guage
and another that tells the computer what the engine temp is. Both of these
could be handled by the same part, but there are many applications where the
engineers use two different senders. You need figure out if the mechanic
changed the right one IF you have two of them.

Then, the guage itself is usually pretty reliable, but they have been known
to fail. If you have been poking around inside the dash installing (a radio
for instance), you may have simply pulled one of the wires off the back of
the guage.

Um, what would the steering wheel have to do with the temperature gauge?

On my 91 F150 4.9 there are two temperature units, one is a sensor up by the
thermostat housing for the computer (the more expensive one) and a sender
for the gauge down on the passenger side of the engine block (about $5 at
O'Reilly's but of course the hardest one to get to). You will need to drain
the coolant down or you will get a shower when you take the sender out. I
put a coat of never seize on the threads of the new sender before screwing
it back in. You can ground the wire to the sender and the gauge will rise to
it's maximum when you turn the ignition key on. I used a jumper wire with an
open spade connector on one end and slid it under the wire terminal that
snaps on the sender. Just ease it up and slide the spade terminal on the
sender stud and push the pickups wiring terminal back down tight. The sender
stud is just like the old ones with a #10 threaded stud but the vehicle
terminal just pushs on like the old ones did. It makes it a lot easier to
ground it out with the jumper because the sender is up in an awkward place
to get to. My gauge just barely moves now and stays on the very low end of
the scale but it "does" move now. It will move up just a little more in the
hot summer when the temperature gets up around 100.

If the heater in your truck has working normally, that
should tell you that the engine is warming into the normal
operating range if not exactly accurate on the temperature
gauge.  If the temperature gauge is not rising at all I
would hope that your mechanic tested the gauge before
replacing the sensor by grounding the wire that attaches to
the sending unit directly to the engine block to determine
whether or not the gauge rises. With the wire completely
grounded to the engine block, the temperature gauge should
go well into the normal range if not all the way to the hot
range. If the gauge does not rise, that is an indication
that there is an electrical problem with the gauge or the
electrical circuit.  Check the voltage from the sender wire
to ground.  If I recall correctly, you should have
approximately 5 volts at that point.  However it is possible
to have as much as system voltage at that point.  I do not
recall which it is on your particular application.  The
important thing is whether or not you have voltage. If you
have the correct voltage at the sender, then a replacement
sender should return to gauge to proper operation.  If it
does not, you likely have a defective gauge that will
require replacement.  The gauges on that vehicle are
supplied in pairs, such that you have to buy another gauge
in addition to the temperature gauge which other gauge is
dependent upon your particular instrument panel
configuration.  If I recall correctly, it is not possible
for the paired gauge to work properly, and the other not
work properly if there is no voltage present on one or the
other of the gauges. You can also test the temperature
sending unit by checking it with an ohm meter. Do this by
checking the sender for resistance before starting the
engine when it is cold. Checked the resistance again when
the engine is completely warmed. You should see a drastic
reduction in the resistance reading.  A good service manual
will provide a resistance chart for various engine coolant
temperatures.

I would hope that your mechanic was knowledgeable enough and
conscientious enough about his work to have done these
simple and quickly conducted test before replacing your
temperature sender.  I also hope that he is aware that your
engine has two temperature sender's.  One is the engine
coolant  temperature sensor for the ECM and the other is for
the engine temperature gauge on the instrument panel. If he
could not distinguish the two he may have replaced the wrong
part with the wrong part.

Cheers,

Lugnut