What kind of solder to use for temperature console resistors?

I need to solder a replacement 510 resistor in my temperature console and found these instructions. However, I am unsure which solder to use. I have a pencil 40W soldering iron.

 

Regular 60/40 rosin core solder will do the job. I prefer the thin stuff, .031 dia.

 

FWIW I spent my working days as an electrical engineer. My first thought when I saw your link was that resistor does not see 3 watts. The total 12 volt supply most likely does not appear across it--therefore no 3 watts dissipated. An electrical overstress usually produces smoke, blackening the part. At any rate, those three resistors hung on in his fix should be secured somehow or vibrations will eventually cause a break in a connection.