Since The Time Machine is told in the first person (or, rather, from two first-person points of view – check out "Narrator Point of View" for more on that), the tone that comes through is the attitude of the two narrators. The two narrators' tones are similar to each other – especially because they are both somewhat fragmented. That is, in parts of the novel the narrators are scientific and precise, but at other times, they are emotional and sentimental.
After the Time Traveller finishes his story, the unnamed narrator notes that, while the story is unbelievable, he isn't sure what to think because the Time Traveller's telling of it was "so credible and sober" (12.25). This description seems fairly accurate to us. For instance, the Time Traveller gives us a step-by-step guide to his scientific investigations: he starts with an observation (there are wells that are sucking air down underground [5.16]); comes up with a theory (the wells might be part of the sanitation system [5.17]); then repeats the process with further observations and further theories.
This scientific method (observe, theorize, repeat) limits what the Time Traveller can tell us or what he can be sure of. Notice how often his theories are accompanied by some caveat like "it seemed to me," which indicates that he's not sure. (Seriously, check it out: we were just flipping through and found "it seemed to me" at 4.24, 4.31, 5.15, and 5.16 – and that's just within a few pages.) The Time Traveller's tone is guided by his interest in being scientific and objective.
While the Time Traveller (and the unnamed narrator, too) may try to be scientific and objective – to give us the facts and nothing but the facts – there are several times when he becomes emotional and acts irrationally. The Time Traveller even notes this himself. For instance, he has trouble looking at the Eloi-Morlock ecology from a scientific point of view because he sympathizes with the Eloi (7.14-15).
While the Time Traveller gets most emotional about the Morlocks and Eloi, there are many other times when he acts irrationally. For instance, while he's traveling through time, he realizes that if he stops, he might cause an explosion. So what does he do? "[W]ith a gust of petulance I resolved to stop forthwith. Like an impatient fool, I lugged over the lever" (3.6). Suddenly he goes from being a thoughtful scientist to being a "petulant," "impatient fool."
In fact, the very beginning of this time travel is marked as being a little irrational: "with a kind of madness growing upon me, I flung myself into futurity" (3.5). Is this someone you would want to be driving your time machine?
There's another emotion that seems really important to this book: awe. Fear may drive the Time Traveller when he deals with the Morlocks, and sympathy when he deals with the Eloi. But when the Time Traveller confronts issues that are bigger than him – bigger than all people or all life – he seems to become awestruck.
Want an example? Check out when he looks out at the stars and realizes how small his concerns are (7.12), or when he sees the world stop spinning and the sky turn red (11.2-3). That's pretty heavy stuff, which never seems to make it into the movie versions. (For some reason, when the main plot of a movie is an adventure to save a woman from monsters, the heroic Time Traveller never turns to the camera and says, "but in the cosmic scheme of things, this isn't really important, because the forces of nature are so much bigger than us.")
What's curious to us is that while some emotions seem opposed to the scientific approach (for instance, the Time Traveller isn't very scientific when he's afraid or sympathetic) awe is tightly wound up with science.