The shown simple circuit was set up on a protoboard and the voltages measured as shown.
Measurements made with a quality digital meter.
Used a stable lab power supply at 12.0VDC. The circuit "on" time is only 12 sec. at a time with 30 sec "off" time.
The measured V drop across the mosfet is 1.6V. Thge power supply indicates 12.0V and 1.8A full-on current. That's about 3W loss at the mosfet (1.8A x 1.6V), but the mosfet doesn't even get warm to the touch.
Why is the V drop across the mosfet so large? The Rds-on is spec'd at only 7mOhm. At 2.5A, that should give a drop of less than 20mV. The applied gate V from the Uno to the mosfet is measured at 5.3V. The mosfet gate V spec is +/-20V max, typical 2-4V, so it should be "full on" with the 5.3V.
I expected to see almost the full 12V at the load, but getting only 9.6V as shown.
Thanks for any help.
IRFB3607PBF is not a logic level FET.
Max 4V Vgs(th) specified when the Id is 100 microamps.
And, want to Rds(on) to 9mΩ, Vgs needs more than 10V.
This is shown in the datasheet as below.
Thank you for the super quick solution. Good thing they are so cheap...I need to order 10 new ones.
If you want to drive directly from the port, try the like following MOSFETs.
e.g. IRL540, IRLZ34, IRLZ44
Yep, the third letter "L" is a proof of Logic Level. 
Note:
Such a high current logic level FET has a large input capacitance(Ciss) and is not suitable for high-speed switching.
A powerful gate drive circuit is required for high-speed switching.
Basically, "Rds(on)" and "Vgs(th)" and "Ciss" are each are conflicting relationships.
DanLRC:
Thank you for the super quick solution. Good thing they are so cheap...I need to order 10 new ones.
Care to run your new choice of MOSFET by us?
Hi,
A complete circuit would help please.
Hand drawn picture would suffice.
Tom... 
Thank you for all the help.
The diagram does show the complete circuit except the Uno board. The board is powered by a 5.3V, 2A charger. The output pin is putting out a measured 5.3V when HIGH. Common ground for circuit.
The circuit simply turns a 4.9ohm hotwire on 8 seconds, and off 30+ seconds.
I have some IRF3708 mosfets. Not "L", but spec shows Rds on=13.5mOhms at Vgs=4.5V and Io=12A. I'm not at all familiar with the details of the specs, but per chrisknightley post above, I'm getting there.
If this wont work, I'll get one of the mosfets suggested above.
Using mosfets vs relays because small size is needed.
After looking at specs for various L level mosfets, I'm even more confused. I need the mosfet to deliver, with 5.3V at the gate, as close to the 12V supply voltage and at about 3A as possible.
Would this one do that, please?
IRL7833PbF
https://www.mouser.com/datasheet/2/196/irl7833pbf-1732797.pdf
DanLRC:
After looking at specs for various L level mosfets, I'm even more confused. I need the mosfet to deliver, with 5.3V at the gate, as close to the 12V supply voltage and at about 3A as possible.
Would this one do that, please?
IRL7833PbF
https://www.mouser.com/datasheet/2/196/irl7833pbf-1732797.pdf
Yes, It is possible.
Also possible with IRF3708.
The "L" rule is not an absolute rule.
As a rough judgment method of whether or not it can be driven at the logic level(5V),
there is something called "Rds(on) at VGS=4.5V is specified".
MOSFETs with Rds(on) listed only at VGS=10V are not recommended for use at the logic level.
If the only on-resistance listing is for Vgs=10V, its not logic level, not even slightly - its not a
case of "not recommended", its simply the wrong component for the job.
If the Vgs given is 5V (or less), its definitely logic level - no judgement is needed, rough or
otherwise!
This, together with the drain-source voltage, is the key specification in the datasheet, you can
ignore the rest when picking a switching MOSFET for on-off switching.
People are often confused by the "threshold voltage" - thinking its the gate drive voltage when it
is not. People also are confused by all the "typical" graphs, thinking they are a guarantee of
performance when they are not. Use the "min" or "max" specifications if you want a guarantee.
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