How to convert skin temperature to core temperature?
The measurement of core temperature (it is the right term*) is easy using an invasive method. It is also reliable since:


  Core temperature is easy to measure and temperatures are relatively
  homogeneous throughout the trunk and head[PMCID: PMC1752199];


However, the measurement of skin temperature is highly dependent on the location of measurement and also ambient temperature, as explained here[DOI: 10.1039/C6EE00456C]:


Also, Xu et. al. concluded in "Relationship between core temperature, skin temperature, and heat flux during exercise in heat" that:


  Algorithms for T_c measurement are location-specific and their
  accuracy is dependent, to a large degree, on sensor placement.


They also proposed two relationships for calculation of T_c based on T_s (Core temp. based on surface temp.) which is included in the paper (regarding copyright laws, I'm not allowed to put it here. you have the DOI and can look it up). 

*Here is the list of few publications which are using "core temperature" to address the temperature inside the body:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1752199/

.../pubmed/23775374

.../pubmed/10655798

Gender Role:
In a study in University of North Texas Source it is concluded that men has different skin temperature, due to different methods of temperature regulation compared to women:


  We found gender differences at four different skin temperature locations. These changes might suggest that men retain more metabolic heat in various locations on the back when exercising in a hot, humid environment compared to women.


Also This Work shows that, although the temperature distribution pattern among genders are similar, women have lower skin temperature. 

This Masters Thesis from University of South Florida indicates findings in regards to clothing and metabolic conditions role on core temperature, i.e. no statistical difference between T_c of genders. Look at Figure 3 in page 23 for heart rate vs. metabolic rates. In page 24 there is a table for measurements for T_c.