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December is the peak of the northeast monsoon in Singapore and the coolest time of the year in any case it is completely implausible that either situation would occur at anytime of the year.
In an alternate global climate 45F is more likely in the event of a near snowball earth only because Singapore would remain above sea level and be more continental in nature as it would be reconnected to the Asian landmass. Any significant warming would remain tempered by rising sea levels and the moderating effect of this.
Maybe not impossible but I wouldn't hold my breath waiting for either one.
Singapore's record high doesn't come nearly to 45 C nor does it's record low come close to 45F. Even during the Pleistocene Glaciation it is unlikely that where Singapore stands today ever got below 45 F even if it occasionally saw less than 50.
And it may not have seen 45 C (113 F) at any time since the most recent Ice Epoch started three million years ago.
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