I think I read somewhere that EA Bowles would hold a bell cloche over a flame to capture warm air and then place it over a Crocus to encourage the flowers to open and allow pollination. A similar arrangement might work for you with the bottomless lemonade bottle and a suitable heat source? 
In terms of fertilisation, it appears there are several factors involved - pollen adhesion, pollen germination, pollen tube growth, ovule receptivity etc. There seems to have been a lot of research on this in fruit trees (peaches, cherries etc). 
Some studies have found that temperature can affect different part of the fertilisation process, i.e. increasing temperature speeds up pollen germination and pollen tube growth in peaches, but reduces stigmatic receptivity (
http://www.ncbi.nlm.nih.gov/pubmed/16163612). 
In cherries pollen germination was inhibited by increasing temperature but not pollen tube growth and the number of pollen tubes reaching the base of the style remained constant across a range of temperature regimes (
http://www.amjbot.org/content/91/4/558.full - this paper cites some sources that look like interesting further reading). 
Genetics also appear to have an effect on pollen germination and tube growth (
www.researchgate.net/publication/222331537_The_effects_of_temperature_on_in_vitro_pollen_germination_and_pollen_tube_growth_of_Pistacia_spp).
Here is a paper on 
Erythronium grandiflorum, which found that "
The number of pollen tubes reaching the base of the style increased rapidly between 24 and 72 hr after pollination and few or no pollen tubes grew to the ovary after 72 hr". It is also suggested that pollen tube growth is inhibited more in self-pollination than when outcrossing. (
http://labs.eeb.utoronto.ca/thomson/publications/Referreed%20Article%20from%20Lab%20Group/Cruzan%20Pollen-tube%20attrition%201989%20Am%20J%20Bot.pdf)
These are not 
Galanthus I know, but they demonstrate that successful fertilisation of the ovules might not be a simple linear relationship with increasing temperature? 
If I were you, I'd just go for it and assume that as the plants are now flowering, temperatures must also be sufficient to allow fertilisation of (at least some of) the ovules.
Good luck!