Changing Temperature may help
There are many reasons for drives to start failing and lowering the temperature may help overheating parts.
My experience with recovering data from a clicking hard drive used the opposite approach, that is I let the hard drive warm up. This system was not used much and with the cooler weather the system was taking a long time to startup or failing to start. So leave the system on for 20 minutes and then restart allowed the recovery or transfer of much of the data to another drive. In this case I had moved the clicking drive to a new system as the slave or secondary drive and waited for the drive to warm up.
There are physical reasons why warm drives work better than cold ones. The spacing between the head and disk decrease with increasing temperature which helps improve the SNR being the main reason in this failure. I would not recommend placing the drive in an oven to warm it up but finding a warm place or leaving the drive on or gently wrapping the drive with a clean cloth (hand towel). An operating drive will consume around 10 to 20 watts and thermally insulating the drive and waiting will increase the temperature.
Of course good luck always helps for your data recovery!