How can I estimate how long will a main sequence star stay on the main sequence given its temperature? I have a generic zero-age main sequence star. The only thing I know about it is its temperature. How can I estimate time time it spends on the main sequence (in millions of years)? I've seen equations that estimate it based on mass, like $L=M^{-2.5}\cdot10^{10}$, but I do not have the mass, only the temperature. Is there any definite formula (accurate to a reasonable degree) for this?
The website on Main sequence stars fromr the Austalian national telescope facility lists star mass, temperature and life span:




Mass/MSun
Luminosity/LSun
T=Effective Temperature/K
Radius/RSun
t=Main sequence lifespan/yrs




0.10
$3×10^{-3}$
2,900
0.16
$2×10^{12}$


0.50
0.03
3,800
0.6
$2×10^{11}$


0.75
0.3
5,000
0.8
$3×10^{10}$


1.0
1
6,000
1.0
$1×10^{10}$


1.5
5
7,000
1.4
$2×10^9$


3
60
11,000
2.5
$2×10^8$


5
600
17,000
3.8
$7×10^7$


10
10,000
22,000
5.6
$2×10^7$


15
17,000
28,000
6.8
$1×10^7$


25
80,000
35,000
8.7
$7×10^6$


60
790,000
44,500
15
$3.4×10^6$




If we suspect a lifespan, $t$ is related to the temperature $T$ by a power relationship, $t=aT^k$, we can plot log(t) against log(T) and look for a linear relationship

That looks plausible, and gives a relationship of $t = 10^{28}\times T^{-4.7}$ (rounding to 2sf)
looking more closely, this tends to underestimate the life span of mid-range stars, but overestimate large and small stars. You can adapt for this by considering smaller and larger stars separately: For stars less than 10000K, a model $t = 10^{37}\times T^{-7.6}$ and for hotter stars $t = 10^{20}\times T^{-3.0}$ gives reasonable fit to the data.
This is, of course, a purely empirical fitting of a curve, and isn't based on an astrophysical model. (though I speculate that the change in gradient is related to the change from the proton-proton to the CNO cycle fusion of hydrogen.)