What diagnostics can you see about the remote site ? Look for temperatures, BUC and LNB currents (mA), receive frequency offset. Receive bit error rate at the remote. At the hub, how well are bursts being received ?
Do the loss of connections really occur with temperature ? What fails ? The outlink reception at the remote or burst reception at the hub. Does the remote modem show RED receive fail alarm light?
The local oscillator in the LNB at the remote site may drift too far off frequency for the remote modem to maintain lock on the outlink carrier. This is most liable to happen if the outlink carrier is small, say 256 kHz wide rather than large like 30 MHz wide. Unstable DRO type LNBs (+/- 2 MHz stability) are fine for satellite TV and wide carriers, like 30MHz. If you have a narrow outlink carrier a higher stability PLL LNB with internal reference crystal is preferred. Most stable is an external reference PLL LNB which uses the stable 10 MHz supply from the indoor modem. Such LNBs are more expensive. Try to have the LNB local oscillator stability less then say 20% of the wanted carrier bandwidth, although there is some flexibility to this. Read the modem receive spec. If you have an unstable DRO LNB it may help to measure its frequency over 24 hours and then adjust the nominal receive frequency slightly to the middle of the range. This is a bodge fix but might help for a particular site. Preferably get a more stable LNB.
The BUC, if very hot, may automatically reduce its output power or turn off to avoid damage. The frequency of the upconverter local oscillator in the BUC is always PLL controlled using an external 10MHz reference from the modem.
High temperatures cause expansion of metal parts. Cable connectors are affected and may become intermittent as the temperature changes. Waggling the cables will make the fault come and go, but don't stand in the beam!.
LNBs and BUCs may simply become faulty if they get too hot. Components do gradually degrade at high temperatures.