The security of temporum is based on the idea that you can convince yourself that several different sources agree on what the time is, with the emphasis on different. Where are the weaknesses in the way it determines if sources are different?
The starting point for temporum is a list of host names to try. It is OK if lots of them fail (e.g. because your device has been switched off on a shelf for years) provided you have a good chance of eventually getting a quorum.
The list of host names is very large, and temporum selects candidates from the list at random. This makes it hard for an attacker to target the particular infrastructure that temporum might use. I hope your device is able to produce decent random numbers immediately after booting!
The list of host names is statically configured. This is important to thwart Sybil attacks: you don't want an attacker to convince you to try a list of apparently-different host names which are all under the attacker's control. Question: can the host list be made dynamic without making it vulnerable?
Hostnames are turned into IP addresses using the DNS. Temporum uses the TLS X.509 PKI to give some assurance that the DNS returned the correct result, about which more below. The DNS isn't security-critical, but if it worries you perhaps temporum could be configured with a list of IP addresses instead - but maybe that will make the device-on-shelf less likely to boot successfully.
Temporum does not compare the IP addresses of "different" host names. This might become a problem once TLS SNI makes large-scale virtual hosting easier. More subtly, there is a risk that temporum happens to query lots of servers that are hosted on the same infrastructure. This can be mitigated by being careful about selecting which host names to include in the list - no more than a few each of Blogspot, Tumblr, Livejournal, GoDaddy vhosts, etc. More than one of each is OK since it helps with on-shelf robustness.
The TLS security model hopes that X.509 certification authorities will only hand out certificates for host names to the organizations that run the hosts. This is a forlorn hope: CAs have had their infrastructure completely compromised; they have handed out intermediate signing certificates to uncontrolled third parties; they are controlled by nation states that treat our information security with contempt.
In the context of temporum, we can reduce this problem by checking that the quorum hosts are authenticated by diverse CAs. Then an attacker would have to compromise multiple CAs to convince us of an incorrect time. Question: are there enough different CAs used by popular sites that temporum can quickly find a usable set?