I would think you can simplify first. For example, there is probably no way to separate the effects of a unique location for a data logger from the possible difference in measurement of each data logger. Thus, using loggeridentity will always conflate its location with differences inherent to each logger. So, first, I would simply look at temperatures over time on a graph to discover if SOME loggers were very far off, and simply remove them from the analysis. Otherwise, they are simply replicates that are not required to have exact same values. Then, your model is simpler. Next, MONTH will clearly have an effect (time, each month has a different mean temperature), so it is not WHETHER month matters, but HOW month matters. I would imagine that you predict that at hotter temperatures, the difference in sites is larger. Of course, that means you want a difference between used and unused habitat. Now, of course, temperature starts low and ends high each day, so most of the day regardless of habitat, temperatures overlap a LOT. Thus, the extremes should be of interest, not the average. And, it would be the extreme UPPER temperatures, not the lower, because only the higher temperatures will influence nesting, because lower temperatures are always within the range that birds can handle. That generates a different kind of question - what is the difference between the maximum temperatures in used and unused habitat, and what is the difference in the duration of high temperatures in both habitats, and how does month influence those differences?  Of course, all this doesn't answer your question. Remember, the normality of residuals assumption is not that restrictive. But, before worrying about that, you should make sure your questions are clear and your need to use repeated measures is correct.

I would think you can simplify first. For example, there is probably no way to separate the effects of a unique location for a data logger from the possible difference in measurement of each data logger. Thus, using loggeridentity will always conflate its location with differences inherent to each logger. So, first, I would simply look at temperatures over time on a graph to discover if SOME loggers were very far off, and simply remove them from the analysis. Otherwise, they are simply replicates that are not required to have exact same values. Then, your model is simpler. Next, MONTH will clearly have an effect (time, each month has a different mean temperature), so it is not WHETHER month matters, but HOW month matters. I would imagine that you predict that at hotter temperatures, the difference in sites is larger. Of course, that means you want a difference between used and unused habitat. Now, of course, temperature starts low and ends high each day, so most of the day regardless of habitat, temperatures overlap a LOT. Thus, the extremes should be of interest, not the average. And, it would be the extreme UPPER temperatures, not the lower, because only the higher temperatures will influence nesting, because lower temperatures are always within the range that birds can handle. That generates a different kind of question - what is the difference between the maximum temperatures in used and unused habitat, and what is the difference in the duration of high temperatures in both habitats, and how does month influence those differences?  Of course, all this doesn't answer your question. Remember, the normality of residuals assumption is not that restrictive. But, before worrying about that, you should make sure your questions are clear and your need to use repeated measures is correct.

Adam Loy and Heike Hofmann have several papers and an R package for checking the assumptions of mixed models. Those papers will be a good start.

Can't understand what you are doing with month in both fixed and random effects?

Is temp per hour / day / month?

You can retain as temp per hour using a Generalized Additive Mixed Model which allows you to model the circular nature of temp over 24 hours. Maybe much more powerful (and convincing) instead of losing all your variation by grouping (i.e. mean values) per day or excluding chunks of the data....

There is a very helpful mixed model R specialist group :

https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

And a really helpful wiki (largely) by Ben Bolker (nice set of examples with code,  see the "Model specification etc." section ):

http://glmm.wikidot.com/faq

Hi everyone, thank you for your comments and suggestions already- I am certainly a neophyte with coding mixed models in R. And for clarification, these nests are turtle nests, specifically for a small freshwater turtle called the Bog Turtle (Glyptemys muhlenbergii). It nests largely in sedge and small clumps of grass, relatively close to the ground. Furthermore, it is not known if this species exhibits temperature dependent sex determination - however, I did not sex hatchlings, so that will be for another study!

James: Thank you for your advice - sometimes, it is easy to lose the forest from the trees, so to speak, with data analysis. I have actually pondered that same point that you have mentioned - that the extremes should matter more than the averages. Some initial plots are suggesting that not only are average temperatures different between nests and random points, but so are maximum and minimum points. At the risk of integrating new knowledge into old questions, it may be worth simply comparing maximum and minimum daily temperatures between used and unused habitat. I still think that a repeated measures design will allow me to account for temperature variation due to time more effectively than other models, but perhaps separately investigating differences in maximum and minimum temperatures may be wise.

Daniel: Thank you for the suggestion - I will look at those papers. It looks like A. M. Loy's doctoral dissertation may be most instructive. Is the package HLMdiag?

Darren: Temperatures were taken every hour, but I was less interested in the daily variation and more interested in monthly variation. 

Regarding your question with month as both a fixed and random effect, I think you are right - it probably should be coded just as a random effect. I suppose the model statement would then be: Temperature= NestorRandom * Month|LoggerIdentity, as I would still expect differences in nest and random points to be partially dependent on monthly variation. I will check out generalized additive mixed models, as factoring in the circular nature of temperature would be useful.

Yes, that is the package I was thinking of!

Another complication is that month has only 3 levels (July, August, September) , which is generally considered to be too little for a random effect (again see : http://glmm.wikidot.com/faq ).

With the quantity and resolution of data you have you may consider using week (12 levels) as the random effect as there is no biologically meaningfull reason to assume any "per month" grouping  .....