This is almost more a science question than a music question. But yes, I think a wooden recorder would be a better choice than plastic, and they're not terribly expensive; they can be had for less than $20 (and even those, in my experience, sound better than similarly-priced plastic ones). It's also interesting to me that you're suggesting subjecting the instrument to more extreme temperatures than would normally be encountered. As a violinist, I would refuse a gig that required me to play outdoors at temperatures below, oh, 45 degrees F or above 80 (I guess... I wouldn't be too happy about the 50s or high 70s either!). If any instrument is going in a freezer or an oven, the experiment might stop being about the effect on pitch and start being about the instrument's ability to avoid damage.
The experiment is a great idea, and there's no reason not to proceed, but to really measure the factors that impact pitch would take very precise measurements of many different factors. You would need to measure not just the outer but inner diameter of the recorder (bore) across all its length; you'd have to measure any gap at joints; you'd need very accurate measurement of the temperature of the air inside the instrument (and, if the experiment is meant to measure realistic use, the impact that warm human breath has on a cold instrument). The recorder is a good choice for keeping it simple; if it were, say, a harpsichord, you'd also be measuring string tension!