I am working with a heat transfer problem having the laser heat source. I tried implementing Temperature dependent convective heat transfer coefficient for the exposed surface of my domain. The nature of this heat transfer coefficient has been described in the figure and the data given below. It was observed that with implementing below model of h=f(Temperature) after the boiling point temp i.e. 3315K the heat transfer solver made several attempts (with reducing increment time size) to find solution for the corresponding and eventually failed with message to many attempts made for this increment. 

However, if i try to omit this model the solver runs smoothly without any issue with max temperature obtained above 3315K . But including this model is physically important. So how can i incorporate this heat coefficient model, having exponential behaviour, without any convergence issue.  

film transfer coefficient = 426.06590576856115 at temperature = 3315.0
film transfer coefficient = 677.8867558884863 at temperature = 3325.0
film transfer coefficient = 1075.5291880803193 at temperature = 3335.0
film transfer coefficient = 1701.6994380595195 at temperature = 3345.0
film transfer coefficient = 2685.0346787661015 at temperature = 3355.0
film transfer coefficient = 4225.070797309474 at temperature = 3365.0
film transfer coefficient = 6630.490564980741 at temperature = 3375.0
film transfer coefficient = 10377.561576622305 at temperature = 3385.0
film transfer coefficient = 16199.188087643406 at temperature = 3395.0
film transfer coefficient = 25220.263057369048 at temperature = 3405.0
film transfer coefficient = 39162.86503311725 at temperature = 3415.0
film transfer coefficient = 60656.550213104194 at temperature = 3425.0
film transfer coefficient = 93706.3831698796 at temperature = 3435.0
film transfer coefficient = 144397.1296273987 at temperature = 3445.0
film transfer coefficient = 221950.1515481647 at temperature = 3455.0
film transfer coefficient = 340305.76529769355 at temperature = 3465.0
film transfer coefficient = 520486.5461643881 at temperature = 3475.0
film transfer coefficient = 794118.4889348152 at temperature = 3485.0
film transfer coefficient = 1208664.7508766854 at temperature = 3495.0
film transfer coefficient = 1835186.4863279662 at temperature = 3505.0
film transfer coefficient = 2779823.930626515 at temperature = 3515.0
film transfer coefficient = 4200741.519660496 at temperature = 3525.0
film transfer coefficient = 6333079.720517894 at temperature = 3535.0
film transfer coefficient = 9525612.702859357 at temperature = 3545.0
film transfer coefficient = 14294481.274501309 at temperature = 3555.0
film transfer coefficient = 21401777.57299162 at temperature = 3565.0
film transfer coefficient = 31970219.178398076 at temperature = 3575.0
film transfer coefficient = 47650116.30439601 at temperature = 3585.0
film transfer coefficient = 70861945.31400956 at temperature = 3595.0
film transfer coefficient = 105147998.37410572 at temperature = 3605.0
film transfer coefficient = 155681057.48935908 at temperature = 3615.0
film transfer coefficient = 229998636.8116503 at temperature = 3625.0
film transfer coefficient = 339060573.0914503 at temperature = 3635.0
film transfer coefficient = 498769158.86488956 at temperature = 3645.0
film transfer coefficient = 732149558.6858958 at temperature = 3655.0
film transfer coefficient = 1072470842.2406694 at temperature = 3665.0
film transfer coefficient = 1567704250.8448846 at temperature = 3675.0
film transfer coefficient = 2286878697.765293 at temperature = 3685.0
film transfer coefficient = 3329122608.837736 at temperature = 3695.0
film transfer coefficient = 4836501839.485471 at temperature = 3705.0