  Including pregnancies, we've been parents now for nearly four and a half years. Through all of it, we've sufficed with our puny underarm thermometer. Within a few weeks of Aidan's birth we learned that 1) it's normal for an infant's head to feel very warm, as long as the actual forehead feels normal, and 2) rectal temperatures cause perfuse liquid bowel movements and upset parents and baby. We're technically minded people so we looked into our gadget options. We found that the reason doctors' offices and nurse lines insist on hearing a rectal temp only is that ear (ca $30) and underarm (ca $2) thermometers each have a margin of error of 1 degree on average and 2 degrees occasionally. However, if you consider that a fever isn't trip to the ER-meriting dangerous unless it's 106 or 107 (in babies, not newborns. I think it's more like 104 in newborns), you can rest assured a temp reading on the underarm up to 104 is within your margin of safety zone. Nobody has spurty BMs, nobody cries. It's taken four years and two kids for us to encounter a situation in which we feel we need a more accurate reading.
I'm still horrified by the memories of rectal insertions and the subsequent bowel-emptying (remember my love affair with our friends, the intestinal flora), so again to gadgets we turn. The urlLink temporal artery thermometer has a margin of error near that of the rectal temp, reads instantly, and involves only the forehead. We've purchased the urlLink Exergen Temporal Scanner ($49 at Walgreens). I'll let you know how it does. 
