Yes any secondary thermometer can be used to double check the temperature - laser temp, wife's meat thermometer, etc. (could get in trouble with the wife if using the latter! )

And I just noticed you are in Tucson. There used to be all sorts of independent radiator repair shops there. They can actually take one apart, repair it, then put it back together! But these days you should be able to go to any auto parts store and get a new radiator for a reasonable price.

Also just seeing the name "Tucson" suggests getting a new radiator anyway - for any older car! You need the engine cooling system to be in tip-top shape to work in the summer there. And even then they don't always work too well with the high summer heat. Stop-and-go city traffic requires a well working electric fan/fan clutch system.

So far as checking the cold start valve, read everything you can find (factory service manual) on how it should work - then see if it is doing so when it should be.

You may find information on that in a search or in a youtube video. Mercedes has similar gadgets for various years, so sometimes searching for [mercedes cold start injector] (leave out year) might find some good videos or information. Searching for a specific year/model will remove a lot of good writeup's.

Also the injection system is called a Bosch KE Jetronic mechanical fuel injection. Other cars like Rolls Royce, Porsche, and others used the same system. So a search for KE Jetronic cold start injector might find some troubleshooting/operation/testing information or videos.

Learn all you can. Read, read read!