I would ask the 3rd party if they are doing tran log backups (or if you can check yourself). If not, then set the database to simple mode and it should not be a problem and it will be kept under control.
I would guess the reason your tran log is growing is some kind of import / process running overnight, possibly even an indexing process, which can be quite intensive.
Basically (I know you said it doesn't interest you but a quick lowdown) a full backup is obviously your last data save at a point in time (i.e. 8 p.m.). If you then take tran logs every hour (when in full mode) then it will save all transactions undertaken during that time period, which causes the log file to grow. It will clear as much as it can when the tran log backup has completed. In simple mode it clears the tran log on a checkpoint (no specific timings but in general it's probably about every 5 seconds) which means you have no backup of the transactions that took place. you CANNOT backup a tranlog when the DB is in simple mode.
Long and the short is if your DB is in simple mode, you can only restore to the last full backup (automated or manual), but if you are in full recovery, then you can restore the last full backup and then any tran logs (I am avoiding diff backups here so you don't get confused) up to a certain point in time.
E.g. (Full mode)
1. Last full backup 8pm Mon
2. Tran logs backups every hour
3. DB dies at 1pm Tues
4. Restore full backup, then each log since and you are up to speed.
(Simple mode)
1. Same crash on the DB
2. No tran log backups so you can only revert to Mon 8pm and all data loaded since will be lost.
HTH,
M.